%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC255+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 : n013.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 3.18s 0.82s
% Output : CNFRefutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 71 ( 12 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 81 ( 26 ~; 19 |; 28 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( singletonP(U)
| ~ singletonP(W)
| ~ 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) )
& ( singletonP(U)
| ~ singletonP(W)
| ~ 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) )
| ( ~ singletonP(U)
& singletonP(W)
& 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(sK1,nil)
& neq(sK3,nil) )
| ( ~ singletonP(sK0)
& singletonP(sK2)
& neq(sK3,nil) ) )
& sK2 = sK0
& sK1 = sK3
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK2,sK1]),skolemize(U,sK0),skolemize(V,sK3),skolemize(W,sK2),skolemize(X,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK1,nil)
| ~ singletonP(sK0) )
& ( ~ neq(sK1,nil)
| singletonP(sK2) )
& neq(sK3,nil)
& sK2 = sK0
& sK1 = sK3
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ssList(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( ~ neq(sK1,nil)
| ~ singletonP(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( ~ neq(sK1,nil)
| singletonP(sK2) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
sK2 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_545,negated_conjecture,
( ~ neq(sK1,nil)
| singletonP(sK0) ),
inference(paramod,[status(thm)],[c_193,c_191]) ).
cnf(c_546,negated_conjecture,
( ~ neq(sK3,nil)
| singletonP(sK0) ),
inference(paramod,[status(thm)],[c_194,c_545]) ).
cnf(c_543,negated_conjecture,
singletonP(sK0),
inference(resolve,[status(thm)],[c_192,c_546]) ).
cnf(c_547,negated_conjecture,
( ~ neq(sK3,nil)
| ~ singletonP(sK0) ),
inference(paramod,[status(thm)],[c_194,c_190]) ).
cnf(c_548,negated_conjecture,
~ neq(sK3,nil),
inference(resolve,[status(thm)],[c_543,c_547]) ).
cnf(c_544,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_192,c_548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC255+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n013.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 12:36:36 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.39 % Process 2755526 was started by sandbox2 on n013,
% 0.13/0.39 % Sat Sep 26 12:36:36 2026
% 0.13/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.41
% 0.18/0.41 % From the command line: assign(max_seconds, 300).
% 3.18/0.82
% 3.18/0.82 % SZS status Theorem for theBenchmark
% 3.18/0.82
% 3.18/0.82 % Proof 1 at 0.39 (+ 0.02) seconds.
% 3.18/0.82 % Length of proof is 8.
% 3.18/0.82 % Level of proof is 3.
% 3.18/0.82 % Maximum clause weight is 10.000.
% 3.18/0.82 % Given clauses 0.
% 3.18/0.82
% 3.18/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------