%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC381+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 : n019.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 08:57:39 AM UTC 2026
% Result : Theorem 32.81s 9.67s
% Output : CNFRefutation 32.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 116 ( 31 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 142 ( 52 ~; 42 |; 38 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 13 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [Z] :
( ssItem(Z)
=> ( ~ memberP(X,Z)
| cons(Z,nil) != W ) )
| ? [Y] :
( memberP(V,Y)
& cons(Y,nil) = U
& ssItem(Y) )
| ~ 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)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [Z] :
( ssItem(Z)
=> ( ~ memberP(X,Z)
| cons(Z,nil) != W ) )
| ? [Y] :
( memberP(V,Y)
& cons(Y,nil) = U
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [Z] :
( memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) )
& ! [Y] :
( ~ memberP(V,Y)
| cons(Y,nil) != U
| ~ ssItem(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,
( ( ( ~ neq(sK0,nil)
& neq(sK4,nil) )
| ( memberP(sK0,sK1)
& cons(sK1,nil) = sK2
& ssItem(sK1)
& ! [Y] :
( ~ memberP(sK4,Y)
| cons(Y,nil) != sK3
| ~ ssItem(Y) )
& neq(sK4,nil) ) )
& sK2 = sK3
& sK0 = sK4
& ssList(sK0)
& ssList(sK2)
& ssList(sK4)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK2,sK0,sK1]),skolemize(U,sK3),skolemize(V,sK4),skolemize(W,sK2),skolemize(X,sK0),skolemize(Z,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK0,nil)
| memberP(sK0,sK1) )
& ( ~ neq(sK0,nil)
| cons(sK1,nil) = sK2 )
& ( ~ neq(sK0,nil)
| ssItem(sK1) )
& ! [VAR_0] :
( ~ neq(sK0,nil)
| ~ memberP(sK4,VAR_0)
| cons(VAR_0,nil) != sK3
| ~ ssItem(VAR_0) )
& neq(sK4,nil)
& sK2 = sK3
& sK0 = sK4
& ssList(sK0)
& ssList(sK2)
& ssList(sK4)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK0,nil)
| memberP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK0,nil)
| cons(sK1,nil) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ neq(sK0,nil)
| ssItem(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( ~ neq(sK0,nil)
| ~ memberP(sK4,A)
| cons(A,nil) != sK3
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
neq(sK4,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK0 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_5221,negated_conjecture,
( ~ neq(sK0,nil)
| cons(sK1,nil) = sK3 ),
inference(paramod,[status(thm)],[c_195,c_191]) ).
cnf(c_5222,negated_conjecture,
( ~ neq(sK4,nil)
| cons(sK1,nil) = sK3 ),
inference(paramod,[status(thm)],[c_196,c_5221]) ).
cnf(c_545,negated_conjecture,
cons(sK1,nil) = sK3,
inference(resolve,[status(thm)],[c_194,c_5222]) ).
cnf(c_5223,negated_conjecture,
( ~ neq(sK4,nil)
| ~ memberP(sK4,A)
| cons(A,nil) != sK3
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_196,c_193]) ).
cnf(c_546,negated_conjecture,
( ~ memberP(sK4,A)
| cons(A,nil) != sK3
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_194,c_5223]) ).
cnf(c_5224,negated_conjecture,
( ~ neq(sK4,nil)
| ssItem(sK1) ),
inference(paramod,[status(thm)],[c_196,c_192]) ).
cnf(c_547,negated_conjecture,
ssItem(sK1),
inference(resolve,[status(thm)],[c_194,c_5224]) ).
cnf(c_5225,negated_conjecture,
( ~ neq(sK0,nil)
| memberP(sK4,sK1) ),
inference(paramod,[status(thm)],[c_196,c_190]) ).
cnf(c_5226,negated_conjecture,
( ~ neq(sK4,nil)
| memberP(sK4,sK1) ),
inference(paramod,[status(thm)],[c_196,c_5225]) ).
cnf(c_548,negated_conjecture,
memberP(sK4,sK1),
inference(resolve,[status(thm)],[c_194,c_5226]) ).
cnf(c_5227,negated_conjecture,
( cons(sK1,nil) != sK3
| ~ ssItem(sK1) ),
inference(resolve,[status(thm)],[c_548,c_546]) ).
cnf(c_5228,negated_conjecture,
( sK3 != sK3
| ~ ssItem(sK1) ),
inference(paramod,[status(thm)],[c_545,c_5227]) ).
cnf(c_5229,negated_conjecture,
~ ssItem(sK1),
inference(copy,[status(thm)],[c_5228]) ).
cnf(c_5220,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_547,c_5229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC381+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.43 % Computer : n019.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Sat Sep 26 12:55:41 UTC 2026
% 0.17/5.43 % CPUTime :
% 0.17/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.44 % Process 1359236 was started by sandbox2 on n019,
% 0.17/5.44 % Sat Sep 26 12:55:41 2026
% 0.17/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.48
% 0.17/5.48 % From the command line: assign(max_seconds, 300).
% 32.81/9.67
% 32.81/9.67 % SZS status Theorem for theBenchmark
% 32.81/9.67
% 32.81/9.67 % Proof 1 at 3.85 (+ 0.30) seconds.
% 32.81/9.67 % Length of proof is 13.
% 32.81/9.67 % Level of proof is 3.
% 32.81/9.67 % Maximum clause weight is 13.000.
% 32.81/9.67 % Given clauses 351.
% 32.81/9.67
% 32.81/9.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------