%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC124-1 : 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 : n001.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 08:56:54 AM UTC 2026
% Result : Unsatisfiable 105.21s 14.49s
% Output : CNFRefutation 105.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 50 ( 24 unt; 0 def)
% Number of atoms : 103 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 63 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_13,axiom,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('theBenchmark.p',co1_13) ).
cnf(c_51,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(clausify,[status(thm)],[co1_13]) ).
fof(co1_12,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_12) ).
cnf(c_52,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_17964,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_53,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_17964]) ).
fof(co1_9,axiom,
app(sk3,sk5) = sk4,
file('theBenchmark.p',co1_9) ).
cnf(c_56,plain,
app(sk3,sk5) = sk4,
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
ssList(sk5),
file('theBenchmark.p',co1_8) ).
cnf(c_57,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_58,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_59,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_60,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_61,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_62,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(clause173,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( segmentP(VAR_3,VAR_1)
| ~ ssList(VAR_3)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| app(app(VAR_0,VAR_1),VAR_2) != VAR_3 ),
file('theBenchmark.p',clause173) ).
cnf(c_72,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(clause115,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ neq(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',clause115) ).
cnf(c_125,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause100,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| neq(VAR_1,VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause100) ).
cnf(c_140,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_157,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_217,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_17965,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_59,c_51]) ).
cnf(c_17966,plain,
( ~ segmentP(sk4,sk1)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_60,c_17965]) ).
cnf(c_323,plain,
( ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_59,c_17966]) ).
cnf(c_324,plain,
neq(sk4,nil),
inference(paramod,[status(thm)],[c_60,c_58]) ).
cnf(c_909,plain,
( segmentP(sk4,B)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != sk4 ),
inference(resolve,[status(thm)],[c_72,c_61]) ).
cnf(c_1326,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_140,c_62]) ).
cnf(c_1382,plain,
app(nil,sk3) = sk3,
inference(resolve,[status(thm)],[c_157,c_62]) ).
cnf(c_17967,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_324,c_125]) ).
cnf(c_17968,plain,
( ~ ssList(sk4)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_217,c_17967]) ).
cnf(c_8273,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_61,c_17968]) ).
cnf(c_8292,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_8273,c_53]) ).
cnf(c_17969,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(paramod,[status(thm)],[c_1382,c_909]) ).
cnf(c_17970,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_217,c_17969]) ).
cnf(c_14547,plain,
( segmentP(sk4,sk3)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_62,c_17970]) ).
cnf(c_17971,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1326,c_217]) ).
cnf(c_17911,plain,
neq(sk3,nil),
inference(resolve,[status(thm)],[c_8292,c_17971]) ).
cnf(c_17941,plain,
~ segmentP(sk4,sk3),
inference(resolve,[status(thm)],[c_17911,c_323]) ).
cnf(c_17951,plain,
( ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_17941,c_14547]) ).
cnf(c_17972,plain,
~ ssList(sk5),
inference(resolve,[status(thm)],[c_17951,c_56]) ).
cnf(c_17963,plain,
$false,
inference(resolve,[status(thm)],[c_57,c_17972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC124-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 12:24:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1779755 was started by sandbox on n001,
% 0.11/0.37 % Sat Sep 26 12:24:43 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 105.21/14.49
% 105.21/14.49 % given #500 (I,wt=40): 559 app(app(A,cons(B,A)),cons(C,D)) != A | -ssList(D) | -ssList(A) | -ssItem(C) | -ssItem(B) | lt(B,C) | lt(C,B) | -lt(skaf59(A),skaf60(A)). [factor(295,c,f)].
% 105.21/14.49
% 105.21/14.49 % given #1000 (A,wt=20): 878 app(A,cons(B,sk4)) != A | -ssList(A) | -ssItem(B) | memberP(A,B). [factor(868,b,d)].
% 105.21/14.49
% 105.21/14.49 % given #1500 (T,wt=8): 16406 neq(sk5,sk4) | sk5 = sk4. [resolve(1324,a,57,a),flip(b)].
% 105.21/14.49
% 105.21/14.49 % SZS status Unsatisfiable for theBenchmark
% 105.21/14.49
% 105.21/14.49 % Proof 1 at 4.56 (+ 1.46) seconds.
% 105.21/14.49 % Length of proof is 27.
% 105.21/14.49 % Level of proof is 7.
% 105.21/14.49 % Maximum clause weight is 26.000.
% 105.21/14.49 % Given clauses 1661.
% 105.21/14.49
% 105.21/14.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------