%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC105+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 : n012.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 08:56:51 AM UTC 2026
% Result : Theorem 18.32s 3.36s
% Output : CNFRefutation 18.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 14 unt; 0 def)
% Number of atoms : 207 ( 83 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 208 ( 63 ~; 88 |; 42 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('theBenchmark.p',ax15) ).
fof(ax48,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(V,U)
& rearsegP(U,V) )
=> U = V ) ) ),
file('theBenchmark.p',ax48) ).
fof(ax51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('theBenchmark.p',ax51) ).
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ( rearsegP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| 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)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ( rearsegP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( rearsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ( ( ( ~ rearsegP(V,U)
| ~ neq(U,nil) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& 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,
( ( ( rearsegP(sK1,sK0)
& neq(sK0,nil) )
| ( nil = sK0
& nil = sK1 ) )
& ( ( ( ~ rearsegP(sK3,sK2)
| ~ neq(sK2,nil) )
& neq(sK3,nil) )
| ( nil != sK2
& nil = sK3 ) )
& sK0 = sK2
& sK1 = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0,sK1]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( rearsegP(sK1,sK0)
| nil = sK0 )
& ( neq(sK0,nil)
| nil = sK0 )
& ( rearsegP(sK1,sK0)
| nil = sK1 )
& ( neq(sK0,nil)
| nil = sK1 )
& ( ~ rearsegP(sK3,sK2)
| ~ neq(sK2,nil)
| nil != sK2 )
& ( neq(sK3,nil)
| nil != sK2 )
& ( ~ rearsegP(sK3,sK2)
| ~ neq(sK2,nil)
| nil = sK3 )
& ( neq(sK3,nil)
| nil = sK3 )
& sK0 = sK2
& sK1 = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_190,negated_conjecture,
( rearsegP(sK1,sK0)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_191,negated_conjecture,
( rearsegP(sK1,sK0)
| sK0 = nil ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_192,negated_conjecture,
( neq(sK0,nil)
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_193,negated_conjecture,
( neq(sK0,nil)
| sK0 = nil ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_194,negated_conjecture,
( rearsegP(sK1,sK0)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_195,negated_conjecture,
( rearsegP(sK1,sK0)
| sK1 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_196,negated_conjecture,
( neq(sK0,nil)
| nil = sK1 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
( neq(sK0,nil)
| sK1 = nil ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_200,negated_conjecture,
( neq(sK3,nil)
| nil != sK2 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
( neq(sK3,nil)
| sK2 != nil ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_202,negated_conjecture,
( ~ rearsegP(sK3,sK2)
| ~ neq(sK2,nil)
| nil = sK3 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_203,negated_conjecture,
( ~ rearsegP(sK3,sK2)
| ~ neq(sK2,nil)
| sK3 = nil ),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_206,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_207,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_208,negated_conjecture,
ssList(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_209,negated_conjecture,
ssList(sK3),
inference(paramod,[status(thm)],[c_207,c_208]) ).
cnf(c_210,negated_conjecture,
ssList(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_211,negated_conjecture,
ssList(sK2),
inference(paramod,[status(thm)],[c_206,c_210]) ).
cnf(c_261,plain,
( rearsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax51]) ).
cnf(c_264,plain,
( B = A
| ~ rearsegP(B,A)
| ~ rearsegP(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax48]) ).
fof(ax17,axiom,
ssList(nil),
file('theBenchmark.p',ax17) ).
cnf(c_307,plain,
ssList(nil),
inference(clausify,[status(thm)],[ax17]) ).
cnf(c_310,plain,
( B != A
| ~ neq(A,B)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[ax15]) ).
cnf(c_4164,negated_conjecture,
( neq(sK0,nil)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_207,c_197]) ).
cnf(c_556,negated_conjecture,
( neq(sK2,nil)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_206,c_4164]) ).
cnf(c_4165,negated_conjecture,
( rearsegP(sK1,sK0)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_207,c_195]) ).
cnf(c_4166,negated_conjecture,
( rearsegP(sK3,sK0)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_207,c_4165]) ).
cnf(c_557,negated_conjecture,
( rearsegP(sK3,sK2)
| sK3 = nil ),
inference(paramod,[status(thm)],[c_206,c_4166]) ).
cnf(c_4167,negated_conjecture,
( neq(sK0,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_206,c_193]) ).
cnf(c_558,negated_conjecture,
( neq(sK2,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_206,c_4167]) ).
cnf(c_4168,negated_conjecture,
( rearsegP(sK1,sK0)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_206,c_191]) ).
cnf(c_4169,negated_conjecture,
( rearsegP(sK3,sK0)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_207,c_4168]) ).
cnf(c_559,negated_conjecture,
( rearsegP(sK3,sK2)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_206,c_4169]) ).
cnf(c_4170,plain,
( A != A
| ~ neq(A,A)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_310]) ).
cnf(c_600,plain,
( ~ neq(A,A)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_4170]) ).
cnf(c_1804,plain,
rearsegP(sK2,nil),
inference(resolve,[status(thm)],[c_261,c_211]) ).
cnf(c_4171,negated_conjecture,
( ~ rearsegP(sK3,sK2)
| sK3 = nil
| sK3 = nil ),
inference(resolve,[status(thm)],[c_556,c_203]) ).
cnf(c_2453,negated_conjecture,
( ~ rearsegP(sK3,sK2)
| sK3 = nil ),
inference(copy,[status(thm)],[c_4171]) ).
cnf(c_2487,plain,
( neq(sK3,nil)
| neq(sK2,nil) ),
inference(resolve,[status(thm)],[c_558,c_201]) ).
cnf(c_4172,negated_conjecture,
( sK3 = sK2
| ~ rearsegP(sK2,sK3)
| ~ ssList(sK3)
| ~ ssList(sK2)
| sK2 = nil ),
inference(resolve,[status(thm)],[c_559,c_264]) ).
cnf(c_4173,negated_conjecture,
( sK3 = sK2
| ~ rearsegP(sK2,sK3)
| ~ ssList(sK3)
| sK2 = nil ),
inference(resolve,[status(thm)],[c_211,c_4172]) ).
cnf(c_2523,negated_conjecture,
( sK3 = sK2
| ~ rearsegP(sK2,sK3)
| sK2 = nil ),
inference(resolve,[status(thm)],[c_209,c_4173]) ).
cnf(c_2648,plain,
~ neq(nil,nil),
inference(resolve,[status(thm)],[c_600,c_307]) ).
cnf(c_4174,negated_conjecture,
( sK3 = nil
| sK3 = nil ),
inference(resolve,[status(thm)],[c_2453,c_557]) ).
cnf(c_4148,negated_conjecture,
sK3 = nil,
inference(copy,[status(thm)],[c_4174]) ).
cnf(c_4175,negated_conjecture,
( sK3 = sK2
| ~ rearsegP(sK2,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_4148,c_2523]) ).
cnf(c_4176,negated_conjecture,
( nil = sK2
| ~ rearsegP(sK2,nil)
| sK2 = nil ),
inference(paramod,[status(thm)],[c_4148,c_4175]) ).
cnf(c_4177,negated_conjecture,
( sK2 = nil
| ~ rearsegP(sK2,nil)
| sK2 = nil ),
inference(copy,[status(thm)],[c_4176]) ).
cnf(c_4178,negated_conjecture,
( ~ rearsegP(sK2,nil)
| sK2 = nil ),
inference(copy,[status(thm)],[c_4177]) ).
cnf(c_4162,negated_conjecture,
sK2 = nil,
inference(resolve,[status(thm)],[c_1804,c_4178]) ).
cnf(c_4179,plain,
( neq(sK3,nil)
| neq(nil,nil) ),
inference(paramod,[status(thm)],[c_4162,c_2487]) ).
cnf(c_4180,plain,
( neq(nil,nil)
| neq(nil,nil) ),
inference(paramod,[status(thm)],[c_4148,c_4179]) ).
cnf(c_4181,plain,
neq(nil,nil),
inference(copy,[status(thm)],[c_4180]) ).
cnf(c_4163,plain,
$false,
inference(resolve,[status(thm)],[c_2648,c_4181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC105+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.97 % Computer : n012.cluster.edu
% 0.08/0.97 % Model : x86_64 x86_64
% 0.08/0.97 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.97 % Memory : 8046.5625MB
% 0.08/0.97 % OS : Linux 6.8.0-71-generic
% 0.08/0.97 % CPULimit : 300
% 0.08/0.97 % WCLimit : 300
% 0.08/0.97 % DateTime : Sat Sep 26 12:15:22 UTC 2026
% 0.08/0.97 % CPUTime :
% 0.08/0.97 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.97 % Process 557645 was started by sandbox2 on n012,
% 0.08/0.97 % Sat Sep 26 12:15:22 2026
% 0.08/0.97 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/1.00
% 0.08/1.00 % From the command line: assign(max_seconds, 300).
% 18.32/3.36
% 18.32/3.36 % given #500 (I,wt=37): 702 -ssList(A) | -ssItem(B) | -ssItem(C) | -ssList(D) | -ssList(E) | app(app(D,cons(B,E)),cons(C,A)) != A | C != B | ssItem(f34(A)). [factor(371,a,f)].
% 18.32/3.36
% 18.32/3.36 % given #1000 (I,wt=32): 1222 -ssList(A) | -ssItem(B) | -ssList(C) | -ssList(D) | app(app(C,cons(B,D)),cons(B,A)) != A | ssList(f37(A)). [factor(723,b,c),xx(f)].
% 18.32/3.36
% 18.32/3.36 % SZS status Theorem for theBenchmark
% 18.32/3.36
% 18.32/3.36 % Proof 1 at 1.95 (+ 0.27) seconds.
% 18.32/3.36 % Length of proof is 39.
% 18.32/3.36 % Level of proof is 7.
% 18.32/3.36 % Maximum clause weight is 15.000.
% 18.32/3.36 % Given clauses 1493.
% 18.32/3.36
% 18.32/3.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------