%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC205+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 : 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 08:57:09 AM UTC 2026
% Result : Theorem 6.97s 1.61s
% Output : CNFRefutation 6.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 88 ( 45 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 89 ( 29 ~; 27 |; 22 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 17 ( 0 sgn 10 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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 = X
& nil != W )
| ( nil = W
& nil != X )
| neq(U,nil)
| ~ 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 = X
& nil != W )
| ( nil = W
& nil != X )
| neq(U,nil)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != X
| nil = W )
& ( nil != W
| nil = X )
& ~ neq(U,nil)
& 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,plain,
( ( nil != sK0
| nil = sK1 )
& ( nil != sK1
| nil = sK0 )
& ~ neq(sK2,nil)
& neq(sK3,nil)
& sK1 = sK2
& sK0 = sK3
& ssList(sK0)
& ssList(sK1)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK1,sK0]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK1),skolemize(X,sK0)],[nnf_87]) ).
cnf(c_192,negated_conjecture,
( nil != sK1
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_1804,negated_conjecture,
( nil != sK1
| sK0 = nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_193,negated_conjecture,
( sK1 != nil
| sK0 = nil ),
inference(copy,[status(thm)],[c_1804]) ).
cnf(c_194,negated_conjecture,
~ neq(sK2,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
neq(sK3,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK1 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK0 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
ssList(sK2),
inference(paramod,[status(thm)],[c_196,c_200]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_297,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_299,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_1805,negated_conjecture,
( sK1 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_197,c_193]) ).
cnf(c_546,negated_conjecture,
( sK2 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_196,c_1805]) ).
cnf(c_1806,negated_conjecture,
( A = sK2
| neq(sK2,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_299,c_201]) ).
cnf(c_1807,negated_conjecture,
( nil = sK2
| neq(sK2,nil) ),
inference(resolve,[status(thm)],[c_1806,c_297]) ).
cnf(c_1808,negated_conjecture,
( sK2 = nil
| neq(sK2,nil) ),
inference(copy,[status(thm)],[c_1807]) ).
cnf(c_1798,negated_conjecture,
sK2 = nil,
inference(resolve,[status(thm)],[c_194,c_1808]) ).
cnf(c_1809,negated_conjecture,
( nil != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_1798,c_546]) ).
cnf(c_1799,negated_conjecture,
sK3 = nil,
inference(copy,[status(thm)],[c_1809]) ).
cnf(c_1801,negated_conjecture,
~ neq(nil,nil),
inference(paramod,[status(thm)],[c_1798,c_194]) ).
cnf(c_1810,negated_conjecture,
neq(nil,nil),
inference(paramod,[status(thm)],[c_1799,c_195]) ).
cnf(c_1803,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1801,c_1810]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC205+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.55 % Computer : n013.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.08/0.55 % CPULimit : 300
% 0.08/0.55 % WCLimit : 300
% 0.08/0.55 % DateTime : Sat Sep 26 12:30:12 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.56 % Process 2732998 was started by sandbox on n013,
% 0.11/0.56 % Sat Sep 26 12:30:12 2026
% 0.11/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.58
% 0.11/0.58 % From the command line: assign(max_seconds, 300).
% 6.97/1.61
% 6.97/1.61 % SZS status Theorem for theBenchmark
% 6.97/1.61
% 6.97/1.61 % Proof 1 at 0.90 (+ 0.07) seconds.
% 6.97/1.61 % Length of proof is 17.
% 6.97/1.61 % Level of proof is 5.
% 6.97/1.61 % Maximum clause weight is 15.000.
% 6.97/1.61 % Given clauses 127.
% 6.97/1.61
% 6.97/1.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------