%------------------------------------------------------------------------------
% 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 : n009.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 : Unsatisfiable 12.05s 1.94s
% Output : CNFRefutation 12.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 22 unt; 0 def)
% Number of atoms : 68 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 34 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_10,axiom,
( segmentP(sk4,sk3)
| nil = sk4 ),
file('theBenchmark.p',co1_10) ).
cnf(c_55,plain,
( segmentP(sk4,sk3)
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_56,plain,
( segmentP(sk4,sk3)
| sk4 = nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_9,axiom,
( neq(sk3,nil)
| nil = sk4 ),
file('theBenchmark.p',co1_9) ).
cnf(c_57,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_58,plain,
( neq(sk3,nil)
| sk4 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_8,axiom,
! [VAR_0] :
( ~ segmentP(sk1,VAR_0)
| ~ segmentP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_59,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_60,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_61,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_62,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_64,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_65,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_66,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
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_127,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause57,axiom,
! [VAR_0] :
( segmentP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause57) ).
cnf(c_170,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_219,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_5752,plain,
( sk4 = nil
| ~ segmentP(sk1,sk3)
| ~ segmentP(sk2,sk3)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_59,c_58]) ).
cnf(c_830,plain,
( sk4 = nil
| ~ segmentP(sk1,sk3)
| ~ segmentP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_64,c_5752]) ).
cnf(c_5753,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_127,c_60]) ).
cnf(c_5754,plain,
( ~ ssList(sk2)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_219,c_5753]) ).
cnf(c_1052,plain,
sk2 != nil,
inference(resolve,[status(thm)],[c_65,c_5754]) ).
cnf(c_1124,plain,
segmentP(sk1,sk1),
inference(resolve,[status(thm)],[c_170,c_66]) ).
cnf(c_4813,plain,
sk4 != nil,
inference(paramod,[status(thm)],[c_62,c_1052]) ).
cnf(c_4841,plain,
( ~ segmentP(sk1,sk3)
| ~ segmentP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_4813,c_830]) ).
cnf(c_4843,plain,
segmentP(sk4,sk3),
inference(resolve,[status(thm)],[c_4813,c_56]) ).
cnf(c_5446,plain,
segmentP(sk1,sk3),
inference(paramod,[status(thm)],[c_61,c_1124]) ).
cnf(c_5447,plain,
~ segmentP(sk2,sk3),
inference(resolve,[status(thm)],[c_5446,c_4841]) ).
cnf(c_5755,plain,
~ segmentP(sk4,sk3),
inference(paramod,[status(thm)],[c_62,c_5447]) ).
cnf(c_5751,plain,
$false,
inference(resolve,[status(thm)],[c_4843,c_5755]) ).
%------------------------------------------------------------------------------
%----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
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 12:13:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 67943 was started by sandbox2 on n009,
% 0.10/0.36 % Sat Sep 26 12:13:14 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 12.05/1.94
% 12.05/1.94 % given #500 (I,wt=35): 559 app(app(A,cons(B,C)),cons(B,D)) != C | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf59(C),skaf60(C)). [factor(298,e,f),merge(g)].
% 12.05/1.94
% 12.05/1.94 % SZS status Unsatisfiable for theBenchmark
% 12.05/1.94
% 12.05/1.94 % Proof 1 at 1.24 (+ 0.29) seconds.
% 12.05/1.94 % Length of proof is 23.
% 12.05/1.94 % Level of proof is 5.
% 12.05/1.94 % Maximum clause weight is 13.000.
% 12.05/1.94 % Given clauses 811.
% 12.05/1.94
% 12.05/1.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------