%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC328+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 : n019.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 08:57:29 AM UTC 2026
% Result : Theorem 6.66s 1.38s
% Output : CNFRefutation 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 12 unt; 0 def)
% Number of atoms : 58 ( 17 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 56 ( 19 ~; 12 |; 16 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 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 : 14 ( 0 sgn 9 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('theBenchmark.p',ax57) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( equalelemsP(U)
& segmentP(V,U) )
| U != W
| V != X
| nil != W ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( equalelemsP(U)
& segmentP(V,U) )
| U != W
| V != X
| nil != W ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ equalelemsP(U)
| ~ segmentP(V,U) )
& W = U
& X = V
& nil = W
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ( ~ equalelemsP(sK1)
| ~ segmentP(sK0,sK1) )
& sK2 = sK1
& sK3 = sK0
& nil = sK2
& ssList(sK3)
& ssList(sK2)
& ssList(sK0)
& ssList(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2,sK3]),skolemize(U,sK1),skolemize(V,sK0),skolemize(W,sK2),skolemize(X,sK3)],[nnf_87]) ).
cnf(c_169,negated_conjecture,
( ~ equalelemsP(sK1)
| ~ segmentP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_170,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_171,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_172,negated_conjecture,
nil = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_1557,negated_conjecture,
nil = sK1,
inference(paramod,[status(thm)],[c_170,c_172]) ).
cnf(c_173,negated_conjecture,
sK1 = nil,
inference(copy,[status(thm)],[c_1557]) ).
cnf(c_174,negated_conjecture,
ssList(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_175,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_171,c_174]) ).
fof(ax74,axiom,
equalelemsP(nil),
file('theBenchmark.p',ax74) ).
cnf(c_207,plain,
equalelemsP(nil),
inference(clausify,[status(thm)],[ax74]) ).
cnf(c_223,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax57]) ).
cnf(c_1558,negated_conjecture,
( ~ equalelemsP(sK1)
| ~ segmentP(sK0,nil) ),
inference(paramod,[status(thm)],[c_173,c_169]) ).
cnf(c_1559,negated_conjecture,
( ~ equalelemsP(nil)
| ~ segmentP(sK0,nil) ),
inference(paramod,[status(thm)],[c_173,c_1558]) ).
cnf(c_486,negated_conjecture,
~ segmentP(sK0,nil),
inference(resolve,[status(thm)],[c_207,c_1559]) ).
cnf(c_1560,negated_conjecture,
segmentP(sK0,nil),
inference(resolve,[status(thm)],[c_223,c_175]) ).
cnf(c_1556,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_486,c_1560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC328+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n019.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 12:48:49 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1345986 was started by sandbox on n019,
% 0.18/0.44 % Sat Sep 26 12:48:49 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 6.66/1.38
% 6.66/1.38 % SZS status Theorem for theBenchmark
% 6.66/1.38
% 6.66/1.38 % Proof 1 at 0.84 (+ 0.05) seconds.
% 6.66/1.38 % Length of proof is 13.
% 6.66/1.38 % Level of proof is 4.
% 6.66/1.38 % Maximum clause weight is 5.000.
% 6.66/1.38 % Given clauses 64.
% 6.66/1.38
% 6.66/1.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------