%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC026+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 08:56:34 AM UTC 2026
% Result : Theorem 14.40s 7.29s
% Output : CNFRefutation 14.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 116 ( 95 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 131 ( 46 ~; 42 |; 35 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 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)
=> ( ( ( nil = V
| nil != U )
& ( nil = U
| nil != V ) )
| ( nil = X
& nil != W )
| ( nil = W
& nil != 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 = V
| nil != U )
& ( nil = U
| nil != V ) )
| ( nil = X
& nil != W )
| ( nil = W
& nil != X )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != V
& nil = U )
| ( nil != U
& nil = V ) )
& ( nil != X
| nil = W )
& ( nil != W
| nil = X )
& 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 = sK3 )
| ( nil != sK3
& nil = sK1 ) )
& ( nil != sK0
| nil = sK2 )
& ( nil != sK2
| nil = sK0 )
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2,sK0]),skolemize(U,sK3),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( nil != sK1
| nil != sK3 )
& ( nil = sK3
| nil = sK1 )
& ( nil != sK0
| nil = sK2 )
& ( nil != sK2
| nil = sK0 )
& sK2 = sK3
& sK0 = sK1
& ssList(sK0)
& ssList(sK2)
& ssList(sK1)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_331,negated_conjecture,
sK0 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_333,negated_conjecture,
( nil != sK2
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2366,negated_conjecture,
( nil != sK2
| nil = sK1 ),
inference(paramod,[status(thm)],[c_331,c_333]) ).
cnf(c_2367,negated_conjecture,
( nil != sK3
| nil = sK1 ),
inference(paramod,[status(thm)],[c_332,c_2366]) ).
cnf(c_2368,negated_conjecture,
( nil != sK3
| sK1 = nil ),
inference(copy,[status(thm)],[c_2367]) ).
cnf(c_334,negated_conjecture,
( sK3 != nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_2368]) ).
cnf(c_335,negated_conjecture,
( nil != sK0
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2369,negated_conjecture,
( nil != sK0
| nil = sK3 ),
inference(paramod,[status(thm)],[c_332,c_335]) ).
cnf(c_2370,negated_conjecture,
( nil != sK1
| nil = sK3 ),
inference(paramod,[status(thm)],[c_331,c_2369]) ).
cnf(c_2371,negated_conjecture,
( nil != sK1
| sK3 = nil ),
inference(copy,[status(thm)],[c_2370]) ).
cnf(c_336,negated_conjecture,
( sK1 != nil
| sK3 = nil ),
inference(copy,[status(thm)],[c_2371]) ).
cnf(c_337,negated_conjecture,
( nil = sK3
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2372,negated_conjecture,
( nil = sK3
| sK1 = nil ),
inference(copy,[status(thm)],[c_337]) ).
cnf(c_338,negated_conjecture,
( sK3 = nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_2372]) ).
cnf(c_339,negated_conjecture,
( nil != sK1
| nil != sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2373,negated_conjecture,
( nil != sK1
| sK3 != nil ),
inference(copy,[status(thm)],[c_339]) ).
cnf(c_340,negated_conjecture,
( sK1 != nil
| sK3 != nil ),
inference(copy,[status(thm)],[c_2373]) ).
cnf(c_2374,negated_conjecture,
( sK3 = nil
| sK3 = nil ),
inference(resolve,[status(thm)],[c_338,c_336]) ).
cnf(c_2363,negated_conjecture,
sK3 = nil,
inference(copy,[status(thm)],[c_2374]) ).
cnf(c_2375,negated_conjecture,
( sK1 = nil
| sK1 = nil ),
inference(resolve,[status(thm)],[c_338,c_334]) ).
cnf(c_2364,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_2375]) ).
cnf(c_2376,negated_conjecture,
( sK1 != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_2363,c_340]) ).
cnf(c_2377,negated_conjecture,
( nil != nil
| nil != nil ),
inference(paramod,[status(thm)],[c_2364,c_2376]) ).
cnf(c_2378,negated_conjecture,
nil != nil,
inference(copy,[status(thm)],[c_2377]) ).
cnf(c_2365,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_2378]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC026+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n014.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 12:05:23 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 3100109 was started by sandbox2 on n014,
% 0.09/5.37 % Sat Sep 26 12:05:23 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.40
% 0.09/5.40 % From the command line: assign(max_seconds, 300).
% 14.40/7.29
% 14.40/7.29 % SZS status Theorem for theBenchmark
% 14.40/7.29
% 14.40/7.29 % Proof 1 at 1.70 (+ 0.15) seconds.
% 14.40/7.29 % Length of proof is 14.
% 14.40/7.29 % Level of proof is 4.
% 14.40/7.29 % Maximum clause weight is 8.000.
% 14.40/7.29 % Given clauses 163.
% 14.40/7.29
% 14.40/7.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------