%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC213+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 : n018.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 08:57:11 AM UTC 2026
% Result : Theorem 12.55s 7.09s
% Output : CNFRefutation 12.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 160 ( 66 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 192 ( 61 ~; 56 |; 60 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 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 : 53 ( 0 sgn 32 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
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)
=> ( ( nil = W
& nil != X )
| neq(U,nil)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X6,cons(X4,nil)) = W
& ssList(X6) )
& app(cons(X4,nil),X5) = Z
& ssList(X5) )
& ssItem(X4) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( app(cons(X1,nil),X3) = W
& ssList(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ equalelemsP(W)
| app(app(Y,W),Z) != X ) ) )
| ~ neq(V,nil)
| 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 )
| neq(U,nil)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X6,cons(X4,nil)) = W
& ssList(X6) )
& app(cons(X4,nil),X5) = Z
& ssList(X5) )
& ssItem(X4) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( app(cons(X1,nil),X3) = W
& ssList(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ equalelemsP(W)
| app(app(Y,W),Z) != X ) ) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ~ neq(U,nil)
& ? [Y] :
( ? [Z] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X6,cons(X4,nil)) != W
| ~ ssList(X6) )
| app(cons(X4,nil),X5) != Z
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( app(cons(X1,nil),X3) != W
| ~ ssList(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& neq(V,nil)
& 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 )
& ~ neq(sK2,nil)
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X6,cons(X4,nil)) != sK1
| ~ ssList(X6) )
| app(cons(X4,nil),X5) != sK5
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( app(cons(X1,nil),X3) != sK1
| ~ ssList(X3) )
| app(X2,cons(X1,nil)) != sK4
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(sK1)
& app(app(sK4,sK1),sK5) = sK0
& ssList(sK5)
& ssList(sK4)
& neq(sK3,nil)
& sK1 = sK2
& sK0 = sK3
& ssList(sK0)
& ssList(sK1)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK1,sK0,sK4,sK5]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK1),skolemize(X,sK0),skolemize(Y,sK4),skolemize(Z,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( nil != sK1
| nil = sK0 )
& ~ neq(sK2,nil)
& ! [VAR_0,VAR_1,VAR_2] :
( app(VAR_2,cons(VAR_0,nil)) != sK1
| ~ 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) != sK1
| ~ ssList(VAR_2)
| app(VAR_1,cons(VAR_0,nil)) != sK4
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) )
& equalelemsP(sK1)
& app(app(sK4,sK1),sK5) = sK0
& ssList(sK5)
& ssList(sK4)
& neq(sK3,nil)
& sK1 = sK2
& sK0 = sK3
& ssList(sK0)
& ssList(sK1)
& ssList(sK3)
& ssList(sK2) ),
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_2053,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_2053]) ).
cnf(c_194,negated_conjecture,
~ neq(sK2,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
sK0 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_206,negated_conjecture,
ssList(sK2),
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_2054,negated_conjecture,
( sK1 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_202,c_193]) ).
cnf(c_559,negated_conjecture,
( sK2 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_201,c_2054]) ).
cnf(c_2055,negated_conjecture,
( A = sK2
| neq(sK2,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_304,c_206]) ).
cnf(c_2056,negated_conjecture,
( nil = sK2
| neq(sK2,nil) ),
inference(resolve,[status(thm)],[c_2055,c_302]) ).
cnf(c_2057,negated_conjecture,
( sK2 = nil
| neq(sK2,nil) ),
inference(copy,[status(thm)],[c_2056]) ).
cnf(c_2027,negated_conjecture,
sK2 = nil,
inference(resolve,[status(thm)],[c_194,c_2057]) ).
cnf(c_2058,negated_conjecture,
( nil != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_2027,c_559]) ).
cnf(c_2037,negated_conjecture,
sK3 = nil,
inference(copy,[status(thm)],[c_2058]) ).
cnf(c_2043,negated_conjecture,
~ neq(nil,nil),
inference(paramod,[status(thm)],[c_2027,c_194]) ).
cnf(c_2059,negated_conjecture,
neq(nil,nil),
inference(paramod,[status(thm)],[c_2037,c_200]) ).
cnf(c_2052,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2043,c_2059]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC213+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n018.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 12:34:12 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 450681 was started by sandbox on n018,
% 0.11/5.39 % Sat Sep 26 12:34:12 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.43
% 0.16/5.43 % From the command line: assign(max_seconds, 300).
% 12.55/7.09
% 12.55/7.09 % SZS status Theorem for theBenchmark
% 12.55/7.09
% 12.55/7.09 % Proof 1 at 1.48 (+ 0.15) seconds.
% 12.55/7.09 % Length of proof is 17.
% 12.55/7.09 % Level of proof is 5.
% 12.55/7.09 % Maximum clause weight is 15.000.
% 12.55/7.09 % Given clauses 129.
% 12.55/7.09
% 12.55/7.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------