%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC103+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 : n020.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 1.71s 0.63s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 94 ( 22 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 110 ( 36 ~; 30 |; 36 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 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 : 12 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( frontsegP(V,U)
& neq(U,nil) )
| ( nil = X
& nil != W )
| ~ 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)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( frontsegP(V,U)
& neq(U,nil) )
| ( nil = X
& nil != W )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| ~ neq(X,nil) )
& ( ~ frontsegP(V,U)
| ~ neq(U,nil) )
& ( nil != X
| nil = W )
& 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_sk,plain,
( ( ( frontsegP(sK0,sK1)
& neq(sK1,nil) )
| ~ neq(sK0,nil) )
& ( ~ frontsegP(sK3,sK2)
| ~ neq(sK2,nil) )
& ( nil != sK0
| nil = sK1 )
& 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]) ).
fof(sk_co1_neg,plain,
( ( frontsegP(sK0,sK1)
| ~ neq(sK0,nil) )
& ( neq(sK1,nil)
| ~ neq(sK0,nil) )
& ( ~ frontsegP(sK3,sK2)
| ~ neq(sK2,nil) )
& ( nil != sK0
| nil = sK1 )
& neq(sK3,nil)
& sK1 = sK2
& sK0 = sK3
& ssList(sK0)
& ssList(sK1)
& ssList(sK3)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( frontsegP(sK0,sK1)
| ~ neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( neq(sK1,nil)
| ~ neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_192,negated_conjecture,
( ~ frontsegP(sK3,sK2)
| ~ 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_1041,negated_conjecture,
( neq(sK1,nil)
| ~ neq(sK3,nil) ),
inference(paramod,[status(thm)],[c_197,c_191]) ).
cnf(c_1042,negated_conjecture,
( neq(sK2,nil)
| ~ neq(sK3,nil) ),
inference(paramod,[status(thm)],[c_196,c_1041]) ).
cnf(c_547,negated_conjecture,
neq(sK2,nil),
inference(resolve,[status(thm)],[c_195,c_1042]) ).
cnf(c_1043,negated_conjecture,
( frontsegP(sK0,sK1)
| ~ neq(sK3,nil) ),
inference(paramod,[status(thm)],[c_197,c_190]) ).
cnf(c_1044,negated_conjecture,
( frontsegP(sK3,sK1)
| ~ neq(sK3,nil) ),
inference(paramod,[status(thm)],[c_197,c_1043]) ).
cnf(c_1045,negated_conjecture,
( frontsegP(sK3,sK2)
| ~ neq(sK3,nil) ),
inference(paramod,[status(thm)],[c_196,c_1044]) ).
cnf(c_548,negated_conjecture,
frontsegP(sK3,sK2),
inference(resolve,[status(thm)],[c_195,c_1045]) ).
cnf(c_1046,negated_conjecture,
~ frontsegP(sK3,sK2),
inference(resolve,[status(thm)],[c_547,c_192]) ).
cnf(c_1040,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_548,c_1046]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC103+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 12:16:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1519298 was started by sandbox2 on n020,
% 0.11/0.37 % Sat Sep 26 12:16:34 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 1.71/0.63
% 1.71/0.63 % SZS status Theorem for theBenchmark
% 1.71/0.63
% 1.71/0.63 % Proof 1 at 0.20 (+ 0.02) seconds.
% 1.71/0.63 % Length of proof is 10.
% 1.71/0.63 % Level of proof is 3.
% 1.71/0.63 % Maximum clause weight is 11.000.
% 1.71/0.63 % Given clauses 0.
% 1.71/0.63
% 1.71/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------