%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC358+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 : n002.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 08:57:35 AM UTC 2026
% Result : Theorem 0.15s 5.55s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 102 ( 35 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 113 ( 36 ~; 33 |; 33 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 16 ( 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)
=> ( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| segmentP(V,U)
| ~ 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)
=> ( ( ( ~ segmentP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| segmentP(V,U)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_90,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( segmentP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ~ segmentP(V,U)
& 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,
( ( ( segmentP(sK1,sK2)
& neq(sK2,nil) )
| ( nil = sK2
& nil = sK1 ) )
& ~ segmentP(sK0,sK3)
& neq(sK0,nil)
& sK2 = sK3
& sK1 = sK0
& ssList(sK1)
& ssList(sK2)
& ssList(sK0)
& ssList(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK0,sK2,sK1]),skolemize(U,sK3),skolemize(V,sK0),skolemize(W,sK2),skolemize(X,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( segmentP(sK1,sK2)
| nil = sK2 )
& ( neq(sK2,nil)
| nil = sK2 )
& ( segmentP(sK1,sK2)
| nil = sK1 )
& ( neq(sK2,nil)
| nil = sK1 )
& ~ segmentP(sK0,sK3)
& neq(sK0,nil)
& sK2 = sK3
& sK1 = sK0
& ssList(sK1)
& ssList(sK2)
& ssList(sK0)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_92,negated_conjecture,
neq(sK0,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_234,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_334,negated_conjecture,
sK1 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_335,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
~ segmentP(sK0,sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_337,negated_conjecture,
( segmentP(sK1,sK2)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_343,negated_conjecture,
( segmentP(sK1,sK2)
| nil = sK0 ),
inference(paramod,[status(thm)],[c_334,c_337]) ).
cnf(c_344,negated_conjecture,
( segmentP(sK0,sK2)
| nil = sK0 ),
inference(paramod,[status(thm)],[c_334,c_343]) ).
cnf(c_345,negated_conjecture,
( segmentP(sK0,sK3)
| nil = sK0 ),
inference(paramod,[status(thm)],[c_335,c_344]) ).
cnf(c_346,negated_conjecture,
( segmentP(sK0,sK3)
| sK0 = nil ),
inference(copy,[status(thm)],[c_345]) ).
cnf(c_338,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_336,c_346]) ).
cnf(c_341,negated_conjecture,
( nil != sK0
| ~ ssList(nil)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_92,c_90]) ).
cnf(c_347,negated_conjecture,
( nil != sK0
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_338,c_341]) ).
cnf(c_348,negated_conjecture,
( nil != nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_338,c_347]) ).
cnf(c_349,negated_conjecture,
( ~ ssList(nil)
| ~ ssList(nil) ),
inference(copy,[status(thm)],[c_348]) ).
cnf(c_350,negated_conjecture,
~ ssList(nil),
inference(copy,[status(thm)],[c_349]) ).
cnf(c_342,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_234,c_350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC358+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.38 % Computer : n002.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Sat Sep 26 12:55:44 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.38 % Process 1771079 was started by sandbox2 on n002,
% 0.12/5.38 % Sat Sep 26 12:55:44 2026
% 0.12/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/5.39
% 0.12/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.55
% 0.15/5.55 % SZS status Theorem for theBenchmark
% 0.15/5.55
% 0.15/5.55 % Proof 1 at 0.14 (+ 0.00) seconds.
% 0.15/5.55 % Length of proof is 12.
% 0.15/5.55 % Level of proof is 3.
% 0.15/5.55 % Maximum clause weight is 5.000.
% 0.15/5.55 % Given clauses 0.
% 0.15/5.55
% 0.15/5.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------