%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC256+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 : n017.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 08:57:17 AM UTC 2026
% Result : Theorem 19.28s 2.93s
% Output : CNFRefutation 19.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 13 unt; 0 def)
% Number of atoms : 128 ( 52 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 134 ( 40 ~; 41 |; 38 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 13 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('theBenchmark.p',ax4) ).
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 )
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| singletonP(U)
| ~ 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 )
& ! [Y] :
( ssItem(Y)
=> ( ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| singletonP(U)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_90,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ~ singletonP(U)
& 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 = sK3
& nil = sK2 )
| ( memberP(sK2,sK4)
& cons(sK4,nil) = sK3
& ssItem(sK4) ) )
& ~ singletonP(sK1)
& neq(sK0,nil)
& sK3 = sK1
& sK2 = sK0
& ssList(sK2)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK3,sK2,sK4]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK3),skolemize(X,sK2),skolemize(Y,sK4)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( nil = sK3
| memberP(sK2,sK4) )
& ( nil = sK2
| memberP(sK2,sK4) )
& ( nil = sK3
| cons(sK4,nil) = sK3 )
& ( nil = sK2
| cons(sK4,nil) = sK3 )
& ( nil = sK3
| ssItem(sK4) )
& ( nil = sK2
| ssItem(sK4) )
& ~ singletonP(sK1)
& neq(sK0,nil)
& sK3 = sK1
& sK2 = sK0
& ssList(sK2)
& ssList(sK3)
& ssList(sK0)
& ssList(sK1) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_92,negated_conjecture,
neq(sK0,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_204,plain,
( cons(B,nil) != A
| ~ ssItem(B)
| singletonP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax4]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_232,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_328,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_329,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK2 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
sK3 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
~ singletonP(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_335,negated_conjecture,
( nil = sK2
| ssItem(sK4) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2563,negated_conjecture,
( nil = sK0
| ssItem(sK4) ),
inference(paramod,[status(thm)],[c_332,c_335]) ).
cnf(c_336,negated_conjecture,
( sK0 = nil
| ssItem(sK4) ),
inference(copy,[status(thm)],[c_2563]) ).
cnf(c_339,negated_conjecture,
( nil = sK2
| cons(sK4,nil) = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2564,negated_conjecture,
( nil = sK2
| cons(sK4,nil) = sK1 ),
inference(paramod,[status(thm)],[c_333,c_339]) ).
cnf(c_2565,negated_conjecture,
( nil = sK0
| cons(sK4,nil) = sK1 ),
inference(paramod,[status(thm)],[c_332,c_2564]) ).
cnf(c_340,negated_conjecture,
( sK0 = nil
| cons(sK4,nil) = sK1 ),
inference(copy,[status(thm)],[c_2565]) ).
cnf(c_347,negated_conjecture,
( nil != sK0
| ~ ssList(nil)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_92,c_90]) ).
cnf(c_2566,negated_conjecture,
( sK0 != nil
| ~ ssList(nil)
| ~ ssList(sK0) ),
inference(copy,[status(thm)],[c_347]) ).
cnf(c_2567,negated_conjecture,
( sK0 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_329,c_2566]) ).
cnf(c_348,negated_conjecture,
sK0 != nil,
inference(resolve,[status(thm)],[c_232,c_2567]) ).
cnf(c_630,negated_conjecture,
cons(sK4,nil) = sK1,
inference(resolve,[status(thm)],[c_348,c_340]) ).
cnf(c_631,negated_conjecture,
ssItem(sK4),
inference(resolve,[status(thm)],[c_348,c_336]) ).
cnf(c_2568,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK1)
| ~ ssList(sK1) ),
inference(resolve,[status(thm)],[c_630,c_204]) ).
cnf(c_2569,negated_conjecture,
( ~ ssItem(sK4)
| singletonP(sK1) ),
inference(resolve,[status(thm)],[c_328,c_2568]) ).
cnf(c_2570,negated_conjecture,
~ ssItem(sK4),
inference(resolve,[status(thm)],[c_334,c_2569]) ).
cnf(c_2562,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_631,c_2570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC256+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n017.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 12:32:33 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 714712 was started by sandbox on n017,
% 0.17/0.44 % Sat Sep 26 12:32:33 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.48
% 0.17/0.48 % From the command line: assign(max_seconds, 300).
% 19.28/2.93
% 19.28/2.93 % SZS status Theorem for theBenchmark
% 19.28/2.93
% 19.28/2.93 % Proof 1 at 2.00 (+ 0.19) seconds.
% 19.28/2.93 % Length of proof is 21.
% 19.28/2.93 % Level of proof is 5.
% 19.28/2.93 % Maximum clause weight is 15.000.
% 19.28/2.93 % Given clauses 421.
% 19.28/2.93
% 19.28/2.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------