%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC086+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 : n026.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 08:56:47 AM UTC 2026
% Result : Theorem 11.10s 1.90s
% Output : CNFRefutation 11.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 141 ( 39 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 154 ( 52 ~; 51 |; 39 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 24 ( 0 sgn 14 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('theBenchmark.p',ax55) ).
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 ) )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ 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 ) )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( segmentP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& 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(sK0,sK1)
& neq(sK1,nil) )
| ( nil = sK1
& nil = sK0 ) )
& ! [Y] :
( ~ segmentP(sK3,Y)
| ~ segmentP(sK2,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK2,nil)
& 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,
( ( segmentP(sK0,sK1)
| nil = sK1 )
& ( neq(sK1,nil)
| nil = sK1 )
& ( segmentP(sK0,sK1)
| nil = sK0 )
& ( neq(sK1,nil)
| nil = sK0 )
& ! [VAR_0] :
( ~ segmentP(sK3,VAR_0)
| ~ segmentP(sK2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) )
& neq(sK2,nil)
& sK1 = sK3
& sK0 = sK2
& ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_194,negated_conjecture,
( segmentP(sK0,sK1)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( segmentP(sK0,sK1)
| sK0 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_196,negated_conjecture,
( neq(sK1,nil)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( neq(sK1,nil)
| sK0 = nil ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_198,negated_conjecture,
( ~ segmentP(sK3,A)
| ~ segmentP(sK2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
neq(sK2,nil),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_202,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
ssList(sK2),
inference(paramod,[status(thm)],[c_201,c_202]) ).
cnf(c_204,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_205,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_200,c_204]) ).
cnf(c_250,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax55]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_301,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_304,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_2055,negated_conjecture,
( neq(sK1,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_201,c_197]) ).
cnf(c_550,negated_conjecture,
( neq(sK3,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_200,c_2055]) ).
cnf(c_2056,negated_conjecture,
( segmentP(sK0,sK1)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_201,c_195]) ).
cnf(c_2057,negated_conjecture,
( segmentP(sK2,sK1)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_201,c_2056]) ).
cnf(c_551,negated_conjecture,
( segmentP(sK2,sK3)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_200,c_2057]) ).
cnf(c_1651,plain,
( ~ segmentP(sK3,sK3)
| ~ segmentP(sK2,sK3)
| ~ neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_205,c_198]) ).
cnf(c_1777,plain,
segmentP(sK3,sK3),
inference(resolve,[status(thm)],[c_250,c_205]) ).
cnf(c_1779,plain,
( ~ segmentP(sK2,sK3)
| ~ neq(sK3,nil) ),
inference(resolve,[status(thm)],[c_1777,c_1651]) ).
cnf(c_2058,negated_conjecture,
( nil != sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolve,[status(thm)],[c_304,c_199]) ).
cnf(c_2059,negated_conjecture,
( sK2 != nil
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(copy,[status(thm)],[c_2058]) ).
cnf(c_2060,negated_conjecture,
( sK2 != nil
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_203,c_2059]) ).
cnf(c_2025,negated_conjecture,
sK2 != nil,
inference(resolve,[status(thm)],[c_301,c_2060]) ).
cnf(c_2052,negated_conjecture,
segmentP(sK2,sK3),
inference(resolve,[status(thm)],[c_2025,c_551]) ).
cnf(c_2053,negated_conjecture,
neq(sK3,nil),
inference(resolve,[status(thm)],[c_2025,c_550]) ).
cnf(c_2061,negated_conjecture,
~ segmentP(sK2,sK3),
inference(resolve,[status(thm)],[c_2053,c_1779]) ).
cnf(c_2054,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2052,c_2061]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC086+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:15:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 941170 was started by sandbox2 on n026,
% 0.09/0.37 % Sat Sep 26 12:15:56 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.39
% 0.14/0.39 % From the command line: assign(max_seconds, 300).
% 11.10/1.90
% 11.10/1.90 % SZS status Theorem for theBenchmark
% 11.10/1.90
% 11.10/1.90 % Proof 1 at 1.36 (+ 0.12) seconds.
% 11.10/1.90 % Length of proof is 27.
% 11.10/1.90 % Level of proof is 5.
% 11.10/1.90 % Maximum clause weight is 13.000.
% 11.10/1.90 % Given clauses 128.
% 11.10/1.90
% 11.10/1.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------