%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC352+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 : n009.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 08:57:33 AM UTC 2026
% Result : Theorem 12.28s 2.04s
% Output : CNFRefutation 12.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 14 unt; 0 def)
% Number of atoms : 114 ( 41 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 118 ( 40 ~; 35 |; 31 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 19 ( 0 sgn 11 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
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(X,W)
| ~ neq(W,nil) )
& neq(X,nil) )
| ( nil = X
& nil != W )
| frontsegP(V,U)
| 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) )
| ( nil = X
& nil != W )
| frontsegP(V,U)
| 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) )
& ( nil != X
| nil = W )
& ~ frontsegP(V,U)
& 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) )
& ( nil != sK0
| nil = sK1 )
& ~ frontsegP(sK2,sK3)
& sK1 = sK3
& sK0 = sK2
& ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK1,sK0]),skolemize(U,sK3),skolemize(V,sK2),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) )
& ( nil != sK0
| nil = sK1 )
& ~ frontsegP(sK2,sK3)
& sK1 = sK3
& sK0 = sK2
& ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3) ),
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_192,negated_conjecture,
( nil != sK0
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_1805,negated_conjecture,
( nil != sK0
| sK1 = nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_193,negated_conjecture,
( sK0 != nil
| sK1 = nil ),
inference(copy,[status(thm)],[c_1805]) ).
cnf(c_194,negated_conjecture,
~ frontsegP(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_196,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_198,negated_conjecture,
ssList(sK2),
inference(paramod,[status(thm)],[c_196,c_197]) ).
cnf(c_262,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax42]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_296,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_298,plain,
( B = A
| neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_1806,negated_conjecture,
( sK0 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_195,c_193]) ).
cnf(c_545,negated_conjecture,
( sK2 != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_196,c_1806]) ).
cnf(c_1807,negated_conjecture,
( frontsegP(sK0,sK1)
| ~ neq(sK2,nil) ),
inference(paramod,[status(thm)],[c_196,c_190]) ).
cnf(c_1808,negated_conjecture,
( frontsegP(sK2,sK1)
| ~ neq(sK2,nil) ),
inference(paramod,[status(thm)],[c_196,c_1807]) ).
cnf(c_1809,negated_conjecture,
( frontsegP(sK2,sK3)
| ~ neq(sK2,nil) ),
inference(paramod,[status(thm)],[c_195,c_1808]) ).
cnf(c_547,negated_conjecture,
~ neq(sK2,nil),
inference(resolve,[status(thm)],[c_194,c_1809]) ).
cnf(c_1759,plain,
frontsegP(nil,nil),
inference(resolve,[status(thm)],[c_296,c_262]) ).
cnf(c_1810,negated_conjecture,
( A = sK2
| neq(sK2,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_298,c_198]) ).
cnf(c_1811,negated_conjecture,
( nil = sK2
| neq(sK2,nil) ),
inference(resolve,[status(thm)],[c_1810,c_296]) ).
cnf(c_1812,negated_conjecture,
( sK2 = nil
| neq(sK2,nil) ),
inference(copy,[status(thm)],[c_1811]) ).
cnf(c_1800,negated_conjecture,
sK2 = nil,
inference(resolve,[status(thm)],[c_547,c_1812]) ).
cnf(c_1813,negated_conjecture,
( nil != nil
| sK3 = nil ),
inference(paramod,[status(thm)],[c_1800,c_545]) ).
cnf(c_1802,negated_conjecture,
sK3 = nil,
inference(copy,[status(thm)],[c_1813]) ).
cnf(c_1814,negated_conjecture,
~ frontsegP(nil,sK3),
inference(paramod,[status(thm)],[c_1800,c_194]) ).
cnf(c_1815,negated_conjecture,
~ frontsegP(nil,nil),
inference(paramod,[status(thm)],[c_1802,c_1814]) ).
cnf(c_1804,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1759,c_1815]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC352+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n009.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 12:51:44 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.42 % Process 171403 was started by sandbox on n009,
% 0.17/0.42 % Sat Sep 26 12:51:44 2026
% 0.17/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 12.28/2.04
% 12.28/2.04 % SZS status Theorem for theBenchmark
% 12.28/2.04
% 12.28/2.04 % Proof 1 at 1.45 (+ 0.10) seconds.
% 12.28/2.04 % Length of proof is 20.
% 12.28/2.04 % Level of proof is 5.
% 12.28/2.04 % Maximum clause weight is 15.000.
% 12.28/2.04 % Given clauses 126.
% 12.28/2.04
% 12.28/2.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------