%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC102+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 : n004.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 08:56:50 AM UTC 2026
% Result : Theorem 5.73s 6.52s
% Output : CNFRefutation 5.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 62 ( 18 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 59 ( 19 ~; 13 |; 18 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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(ax42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('theBenchmark.p',ax42) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( frontsegP(V,U)
& neq(U,nil) )
| ~ neq(V,nil)
| X != W
| 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)
=> ( ( frontsegP(V,U)
& neq(U,nil) )
| ~ neq(V,nil)
| X != W
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ frontsegP(V,U)
| ~ neq(U,nil) )
& neq(V,nil)
& X = W
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil) )
& neq(sK1,nil)
& sK2 = sK3
& sK3 = sK0
& sK2 = sK1
& ssList(sK2)
& ssList(sK3)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK2)],[nnf_87]) ).
cnf(c_190,negated_conjecture,
( ~ frontsegP(sK1,sK0)
| ~ neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
neq(sK1,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
sK3 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_194,negated_conjecture,
sK2 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_1684,negated_conjecture,
sK3 = sK1,
inference(paramod,[status(thm)],[c_192,c_194]) ).
cnf(c_1685,negated_conjecture,
sK0 = sK1,
inference(paramod,[status(thm)],[c_193,c_1684]) ).
cnf(c_195,negated_conjecture,
sK1 = sK0,
inference(copy,[status(thm)],[c_1685]) ).
cnf(c_196,negated_conjecture,
ssList(sK2),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_1686,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_192,c_196]) ).
cnf(c_197,negated_conjecture,
ssList(sK0),
inference(paramod,[status(thm)],[c_193,c_1686]) ).
cnf(c_261,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax42]) ).
cnf(c_545,negated_conjecture,
neq(sK0,nil),
inference(paramod,[status(thm)],[c_195,c_191]) ).
cnf(c_1687,negated_conjecture,
( ~ frontsegP(sK0,sK0)
| ~ neq(sK0,nil) ),
inference(paramod,[status(thm)],[c_195,c_190]) ).
cnf(c_546,negated_conjecture,
~ frontsegP(sK0,sK0),
inference(resolve,[status(thm)],[c_545,c_1687]) ).
cnf(c_1688,negated_conjecture,
frontsegP(sK0,sK0),
inference(resolve,[status(thm)],[c_261,c_197]) ).
cnf(c_1683,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_546,c_1688]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC102+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.66 % Computer : n004.cluster.edu
% 0.18/5.66 % Model : x86_64 x86_64
% 0.18/5.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.66 % Memory : 8046.5625MB
% 0.18/5.66 % OS : Linux 6.8.0-71-generic
% 0.18/5.66 % CPULimit : 300
% 0.18/5.66 % WCLimit : 300
% 0.18/5.66 % DateTime : Sat Sep 26 12:15:28 UTC 2026
% 0.18/5.67 % CPUTime :
% 0.18/5.67 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.67 % Process 1670966 was started by sandbox2 on n004,
% 0.18/5.67 % Sat Sep 26 12:15:28 2026
% 0.18/5.67 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.23/5.71
% 0.23/5.71 % From the command line: assign(max_seconds, 300).
% 5.73/6.52
% 5.73/6.52 % SZS status Theorem for theBenchmark
% 5.73/6.52
% 5.73/6.52 % Proof 1 at 0.72 (+ 0.07) seconds.
% 5.73/6.52 % Length of proof is 14.
% 5.73/6.52 % Level of proof is 5.
% 5.73/6.52 % Maximum clause weight is 11.000.
% 5.73/6.52 % Given clauses 88.
% 5.73/6.52
% 5.73/6.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------