%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC037+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 : n007.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 08:56:37 AM UTC 2026
% Result : Theorem 4.54s 1.07s
% Output : CNFRefutation 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 149 ( 69 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 159 ( 49 ~; 54 |; 41 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn 13 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('theBenchmark.p',ax58) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssList(Y)
=> ( ~ segmentP(W,Y)
| ~ segmentP(X,Y)
| ~ neq(Y,nil) ) ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssList(Y)
=> ( ~ segmentP(W,Y)
| ~ segmentP(X,Y)
| ~ neq(Y,nil) ) ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
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] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( segmentP(W,Y)
& segmentP(X,Y)
& neq(Y,nil)
& ssList(Y) ) )
& nil != U
& W = U
& X = V
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg_sk,plain,
( ( ( nil = sK1
& nil = sK3 )
| ( segmentP(sK1,sK0)
& segmentP(sK3,sK0)
& neq(sK0,nil)
& ssList(sK0) ) )
& nil != sK4
& sK1 = sK4
& sK3 = sK2
& nil = sK2
& ssList(sK3)
& ssList(sK1)
& ssList(sK2)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK2,sK1,sK3,sK0]),skolemize(U,sK4),skolemize(V,sK2),skolemize(W,sK1),skolemize(X,sK3),skolemize(Y,sK0)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( nil = sK1
| segmentP(sK1,sK0) )
& ( nil = sK3
| segmentP(sK1,sK0) )
& ( nil = sK1
| segmentP(sK3,sK0) )
& ( nil = sK3
| segmentP(sK3,sK0) )
& ( nil = sK1
| neq(sK0,nil) )
& ( nil = sK3
| neq(sK0,nil) )
& ( nil = sK1
| ssList(sK0) )
& ( nil = sK3
| ssList(sK0) )
& nil != sK4
& sK1 = sK4
& sK3 = sK2
& nil = sK2
& ssList(sK3)
& ssList(sK1)
& ssList(sK2)
& ssList(sK4) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_93,negated_conjecture,
( nil = sK1
| neq(sK0,nil) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_233,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_287,plain,
( nil = A
| ~ segmentP(nil,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_333,negated_conjecture,
nil = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_334,negated_conjecture,
sK2 = nil,
inference(copy,[status(thm)],[c_333]) ).
cnf(c_335,negated_conjecture,
sK3 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_336,negated_conjecture,
sK3 = nil,
inference(paramod,[status(thm)],[c_334,c_335]) ).
cnf(c_337,negated_conjecture,
sK1 = sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_338,negated_conjecture,
nil != sK4,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_339,negated_conjecture,
sK4 != nil,
inference(copy,[status(thm)],[c_338]) ).
cnf(c_341,negated_conjecture,
( nil = sK1
| ssList(sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2194,negated_conjecture,
( nil = sK4
| ssList(sK0) ),
inference(paramod,[status(thm)],[c_337,c_341]) ).
cnf(c_2195,negated_conjecture,
( sK4 = nil
| ssList(sK0) ),
inference(copy,[status(thm)],[c_2194]) ).
cnf(c_342,negated_conjecture,
ssList(sK0),
inference(resolve,[status(thm)],[c_339,c_2195]) ).
cnf(c_344,negated_conjecture,
( nil = sK1
| segmentP(sK3,sK0) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_2196,negated_conjecture,
( nil = sK1
| segmentP(nil,sK0) ),
inference(paramod,[status(thm)],[c_336,c_344]) ).
cnf(c_2197,negated_conjecture,
( nil = sK4
| segmentP(nil,sK0) ),
inference(paramod,[status(thm)],[c_337,c_2196]) ).
cnf(c_2198,negated_conjecture,
( sK4 = nil
| segmentP(nil,sK0) ),
inference(copy,[status(thm)],[c_2197]) ).
cnf(c_345,negated_conjecture,
segmentP(nil,sK0),
inference(resolve,[status(thm)],[c_339,c_2198]) ).
cnf(c_351,negated_conjecture,
( nil != sK0
| ~ ssList(nil)
| ~ ssList(sK0)
| nil = sK1 ),
inference(resolve,[status(thm)],[c_93,c_90]) ).
cnf(c_2199,negated_conjecture,
( nil != sK0
| ~ ssList(nil)
| ~ ssList(sK0)
| nil = sK4 ),
inference(paramod,[status(thm)],[c_337,c_351]) ).
cnf(c_2200,negated_conjecture,
( nil != sK0
| ~ ssList(nil)
| ~ ssList(sK0)
| sK4 = nil ),
inference(copy,[status(thm)],[c_2199]) ).
cnf(c_2201,negated_conjecture,
( sK0 != nil
| ~ ssList(nil)
| ~ ssList(sK0)
| sK4 = nil ),
inference(copy,[status(thm)],[c_2200]) ).
cnf(c_2202,negated_conjecture,
( sK0 != nil
| ~ ssList(nil)
| ~ ssList(sK0) ),
inference(resolve,[status(thm)],[c_339,c_2201]) ).
cnf(c_2203,negated_conjecture,
( sK0 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_342,c_2202]) ).
cnf(c_352,negated_conjecture,
sK0 != nil,
inference(resolve,[status(thm)],[c_233,c_2203]) ).
cnf(c_2204,negated_conjecture,
( nil = sK0
| ~ segmentP(nil,sK0) ),
inference(resolve,[status(thm)],[c_342,c_287]) ).
cnf(c_2205,negated_conjecture,
( sK0 = nil
| ~ segmentP(nil,sK0) ),
inference(copy,[status(thm)],[c_2204]) ).
cnf(c_2206,negated_conjecture,
sK0 = nil,
inference(resolve,[status(thm)],[c_345,c_2205]) ).
cnf(c_2193,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_352,c_2206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC037+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 12:04:39 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 3671965 was started by sandbox2 on n007,
% 0.11/0.36 % Sat Sep 26 12:04:39 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 4.54/1.07
% 4.54/1.07 % SZS status Theorem for theBenchmark
% 4.54/1.07
% 4.54/1.07 % Proof 1 at 0.59 (+ 0.05) seconds.
% 4.54/1.07 % Length of proof is 21.
% 4.54/1.07 % Level of proof is 5.
% 4.54/1.07 % Maximum clause weight is 10.000.
% 4.54/1.07 % Given clauses 162.
% 4.54/1.07
% 4.54/1.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------