%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC059-1 : 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 : 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 08:56:42 AM UTC 2026
% Result : Unsatisfiable 32.08s 4.60s
% Output : CNFRefutation 32.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 56 ( 20 unt; 0 def)
% Number of atoms : 112 ( 40 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 109 ( 53 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 9 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_12) ).
cnf(c_53,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_54,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_53]) ).
fof(co1_11,axiom,
! [VAR_0] :
( ~ segmentP(sk1,VAR_0)
| ~ segmentP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sk2 ),
file('theBenchmark.p',co1_11) ).
cnf(c_55,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_56,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_10,axiom,
( neq(sk2,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_10) ).
cnf(c_57,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_58,plain,
( neq(sk2,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_9,axiom,
( segmentP(sk4,sk3)
| ~ neq(sk4,nil) ),
file('theBenchmark.p',co1_9) ).
cnf(c_59,plain,
( segmentP(sk4,sk3)
| ~ neq(sk4,nil) ),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
file('theBenchmark.p',co1_8) ).
cnf(c_60,plain,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
( nil != sk4
| nil = sk3 ),
file('theBenchmark.p',co1_7) ).
cnf(c_61,plain,
( nil != sk4
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_14398,plain,
( nil != sk4
| sk3 = nil ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_62,plain,
( sk4 != nil
| sk3 = nil ),
inference(copy,[status(thm)],[c_14398]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_63,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_64,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_65,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_64]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_67,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_68,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_69,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_130,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_173,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_222,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_834,plain,
( neq(sk2,nil)
| sk3 != nil ),
inference(paramod,[status(thm)],[c_63,c_54]) ).
cnf(c_835,plain,
( segmentP(sk4,sk3)
| ~ neq(sk2,nil) ),
inference(paramod,[status(thm)],[c_65,c_59]) ).
cnf(c_836,plain,
( neq(sk3,nil)
| ~ neq(sk2,nil) ),
inference(paramod,[status(thm)],[c_65,c_60]) ).
cnf(c_837,plain,
( sk2 != nil
| sk3 = nil ),
inference(paramod,[status(thm)],[c_65,c_62]) ).
cnf(c_1110,plain,
segmentP(sk1,sk1),
inference(resolve,[status(thm)],[c_173,c_69]) ).
cnf(c_11497,plain,
( sk2 = nil
| segmentP(sk4,sk3) ),
inference(resolve,[status(thm)],[c_835,c_58]) ).
cnf(c_11570,plain,
( sk2 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_836,c_58]) ).
cnf(c_11571,plain,
( neq(sk2,nil)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_837,c_58]) ).
cnf(c_11727,plain,
segmentP(sk1,sk3),
inference(paramod,[status(thm)],[c_63,c_1110]) ).
cnf(c_14046,plain,
( sk2 = nil
| segmentP(sk2,sk3) ),
inference(paramod,[status(thm)],[c_65,c_11497]) ).
cnf(c_14399,plain,
( ~ segmentP(sk1,sk3)
| ~ segmentP(sk2,sk3)
| ~ ssList(sk3)
| sk2 = nil
| sk2 = nil ),
inference(resolve,[status(thm)],[c_11570,c_56]) ).
cnf(c_14400,plain,
( ~ segmentP(sk1,sk3)
| ~ segmentP(sk2,sk3)
| ~ ssList(sk3)
| sk2 = nil ),
inference(copy,[status(thm)],[c_14399]) ).
cnf(c_14401,plain,
( ~ segmentP(sk1,sk3)
| ~ segmentP(sk2,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_67,c_14400]) ).
cnf(c_14049,plain,
( ~ segmentP(sk2,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_11727,c_14401]) ).
cnf(c_14402,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_11571,c_834]) ).
cnf(c_14389,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_14402]) ).
cnf(c_14403,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_14389,c_130]) ).
cnf(c_14404,plain,
( ~ ssList(sk2)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_222,c_14403]) ).
cnf(c_14393,plain,
sk2 != nil,
inference(resolve,[status(thm)],[c_68,c_14404]) ).
cnf(c_14395,plain,
~ segmentP(sk2,sk3),
inference(resolve,[status(thm)],[c_14393,c_14049]) ).
cnf(c_14405,plain,
sk2 = nil,
inference(resolve,[status(thm)],[c_14395,c_14046]) ).
cnf(c_14397,plain,
$false,
inference(resolve,[status(thm)],[c_14393,c_14405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC059-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 12:12:10 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 934894 was started by sandbox on n026,
% 0.18/0.45 % Sat Sep 26 12:12:10 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 32.08/4.60
% 32.08/4.60 % given #500 (I,wt=66): 566 app(app(A,cons(B,C)),cons(D,C)) != A | -ssList(C) | -ssList(A) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | app(app(skaf61(A),cons(skaf59(A),skaf62(A))),cons(skaf60(A),skaf63(A))) = A. [factor(304,c,f)].
% 32.08/4.60
% 32.08/4.60 % SZS status Unsatisfiable for theBenchmark
% 32.08/4.60
% 32.08/4.60 % Proof 1 at 3.61 (+ 0.46) seconds.
% 32.08/4.60 % Length of proof is 34.
% 32.08/4.60 % Level of proof is 7.
% 32.08/4.60 % Maximum clause weight is 19.000.
% 32.08/4.60 % Given clauses 893.
% 32.08/4.60
% 32.08/4.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------