%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC007-1 : 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 : 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 08:56:31 AM UTC 2026
% Result : Unsatisfiable 26.15s 4.25s
% Output : CNFRefutation 26.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 59 ( 28 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 72 ( 41 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_49,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause73,axiom,
! [VAR_0] :
( app(VAR_0,nil) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause73) ).
cnf(c_108,plain,
( app(A,nil) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause73]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_109,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_199,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_5,axiom,
nil = sk3,
file('theBenchmark.p',co1_5) ).
cnf(c_202,plain,
nil = sk3,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_203,plain,
sk3 = nil,
inference(copy,[status(thm)],[c_202]) ).
fof(co1_7,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_7) ).
cnf(c_206,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_207,plain,
sk1 = nil,
inference(paramod,[status(thm)],[c_203,c_206]) ).
fof(co1_8,axiom,
! [VAR_0,VAR_1,VAR_2] :
( app(VAR_0,VAR_2) != sk1
| app(app(VAR_0,VAR_1),VAR_2) != sk2
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_208,plain,
( app(A,C) != sk1
| app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_209,plain,
( app(A,C) != nil
| app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_207,c_208]) ).
cnf(c_360,plain,
( app(A,A) != nil
| app(app(A,B),A) != sk2
| ~ ssList(B)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_209]) ).
cnf(c_1113,plain,
app(nil,nil) = nil,
inference(resolve,[status(thm)],[c_108,c_49]) ).
cnf(c_7067,plain,
app(nil,sk2) = sk2,
inference(resolve,[status(thm)],[c_199,c_109]) ).
cnf(c_7068,plain,
app(sk2,nil) = sk2,
inference(resolve,[status(thm)],[c_199,c_108]) ).
cnf(c_11765,plain,
( app(nil,nil) != nil
| app(sk2,nil) != sk2
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_7067,c_360]) ).
cnf(c_11766,plain,
( app(nil,nil) != nil
| sk2 != sk2
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_7068,c_11765]) ).
cnf(c_11767,plain,
( nil != nil
| sk2 != sk2
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramod,[status(thm)],[c_1113,c_11766]) ).
cnf(c_11768,plain,
( nil != nil
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(copy,[status(thm)],[c_11767]) ).
cnf(c_11769,plain,
( ~ ssList(sk2)
| ~ ssList(nil) ),
inference(copy,[status(thm)],[c_11768]) ).
cnf(c_11770,plain,
~ ssList(sk2),
inference(resolve,[status(thm)],[c_49,c_11769]) ).
cnf(c_11764,plain,
$false,
inference(resolve,[status(thm)],[c_199,c_11770]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC007-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n007.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 12:01:09 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3663672 was started by sandbox on n007,
% 0.16/0.43 % Sat Sep 26 12:01:09 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 26.15/4.25
% 26.15/4.25 % given #500 (I,wt=40): 559 app(A,cons(B,cons(C,cons(C,nil)))) != cons(C,nil) | -ssList(cons(C,nil)) | -ssList(A) | -ssItem(C) | -ssItem(B) | B = C. [factor(370,d,g)].
% 26.15/4.25
% 26.15/4.25 % given #1000 (F,wt=11): 10184 app(sk2,A) != nil | -ssList(A). [back_unit_del(7042),unit_del(c,10173)].
% 26.15/4.25
% 26.15/4.25 % SZS status Unsatisfiable for theBenchmark
% 26.15/4.25
% 26.15/4.25 % Proof 1 at 2.90 (+ 0.84) seconds.
% 26.15/4.25 % Length of proof is 15.
% 26.15/4.25 % Level of proof is 5.
% 26.15/4.25 % Maximum clause weight is 26.000.
% 26.15/4.25 % Given clauses 1104.
% 26.15/4.25
% 26.15/4.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------