%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC036+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 : n011.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 08:56:37 AM UTC 2026
% Result : Theorem 3.32s 1.14s
% Output : CNFRefutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 57 ( 40 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 59 ( 19 ~; 14 |; 18 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 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 = X
& nil != W )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = X
& nil != W )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != X
| nil = W )
& nil != U
& W = U
& X = V
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ( nil != sK1
| nil = sK2 )
& nil != sK3
& sK2 = sK3
& sK1 = sK0
& nil = sK0
& ssList(sK1)
& ssList(sK2)
& ssList(sK0)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK0,sK2,sK1]),skolemize(U,sK3),skolemize(V,sK0),skolemize(W,sK2),skolemize(X,sK1)],[nnf_87]) ).
cnf(c_331,negated_conjecture,
nil = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_332,negated_conjecture,
sK0 = nil,
inference(copy,[status(thm)],[c_331]) ).
cnf(c_333,negated_conjecture,
sK1 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
sK1 = nil,
inference(paramod,[status(thm)],[c_332,c_333]) ).
cnf(c_335,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
nil != sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_337,negated_conjecture,
sK3 != nil,
inference(copy,[status(thm)],[c_336]) ).
cnf(c_338,negated_conjecture,
( nil != sK1
| nil = sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_340,negated_conjecture,
( nil != sK1
| nil = sK3 ),
inference(paramod,[status(thm)],[c_335,c_338]) ).
cnf(c_341,negated_conjecture,
( nil != nil
| nil = sK3 ),
inference(paramod,[status(thm)],[c_334,c_340]) ).
cnf(c_342,negated_conjecture,
( nil != nil
| sK3 = nil ),
inference(copy,[status(thm)],[c_341]) ).
cnf(c_343,negated_conjecture,
sK3 = nil,
inference(copy,[status(thm)],[c_342]) ).
cnf(c_339,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_337,c_343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC036+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.63 % Computer : n011.cluster.edu
% 0.17/0.63 % Model : x86_64 x86_64
% 0.17/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.63 % Memory : 8046.5625MB
% 0.17/0.63 % OS : Linux 6.8.0-71-generic
% 0.17/0.63 % CPULimit : 300
% 0.17/0.63 % WCLimit : 300
% 0.17/0.63 % DateTime : Sat Sep 26 12:06:31 UTC 2026
% 0.17/0.64 % CPUTime :
% 0.17/0.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.64 % Process 457665 was started by sandbox2 on n011,
% 0.17/0.64 % Sat Sep 26 12:06:31 2026
% 0.17/0.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.68
% 0.20/0.68 % From the command line: assign(max_seconds, 300).
% 3.32/1.14
% 3.32/1.14 % SZS status Theorem for theBenchmark
% 3.32/1.14
% 3.32/1.14 % Proof 1 at 0.44 (+ 0.00) seconds.
% 3.32/1.14 % Length of proof is 10.
% 3.32/1.14 % Level of proof is 4.
% 3.32/1.14 % Maximum clause weight is 8.000.
% 3.32/1.14 % Given clauses 0.
% 3.32/1.14
% 3.32/1.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------