%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC017-1 : 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 : n016.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 08:56:33 AM UTC 2026
% Result : Unsatisfiable 26.71s 20.47s
% Output : CNFRefutation 26.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 85 ( 28 unt; 0 def)
% Number of atoms : 205 ( 68 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 217 ( 97 ~; 120 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 29 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_14,axiom,
( frontsegP(sk4,sk3)
| nil = sk3 ),
file('theBenchmark.p',co1_14) ).
cnf(c_51,plain,
( frontsegP(sk4,sk3)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_52,plain,
( frontsegP(sk4,sk3)
| sk3 = nil ),
inference(copy,[status(thm)],[c_51]) ).
fof(co1_13,axiom,
( neq(sk3,nil)
| nil = sk3 ),
file('theBenchmark.p',co1_13) ).
cnf(c_53,plain,
( neq(sk3,nil)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_54,plain,
( neq(sk3,nil)
| sk3 = nil ),
inference(copy,[status(thm)],[c_53]) ).
fof(co1_11,axiom,
( neq(sk3,nil)
| nil = sk4 ),
file('theBenchmark.p',co1_11) ).
cnf(c_57,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_58,plain,
( neq(sk3,nil)
| sk4 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_9,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_9) ).
cnf(c_61,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_62,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_61]) ).
fof(co1_8,axiom,
! [VAR_0] :
( ~ frontsegP(sk1,VAR_0)
| ~ frontsegP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sk2 ),
file('theBenchmark.p',co1_8) ).
cnf(c_63,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_64,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(copy,[status(thm)],[c_63]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_67,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_68,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_69,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_68]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_70,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_71,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_72,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_73,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(clause154,axiom,
! [VAR_0,VAR_1,VAR_2] :
( frontsegP(VAR_0,VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_2)
| ~ frontsegP(VAR_1,VAR_2)
| ~ frontsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause154) ).
cnf(c_97,plain,
( frontsegP(A,C)
| ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ~ frontsegP(B,C)
| ~ frontsegP(A,B) ),
inference(clausify,[status(thm)],[clause154]) ).
fof(clause129,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ frontsegP(VAR_1,VAR_0)
| ~ frontsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause129) ).
cnf(c_121,plain,
( B = A
| ~ ssList(B)
| ~ ssList(A)
| ~ frontsegP(B,A)
| ~ frontsegP(A,B) ),
inference(clausify,[status(thm)],[clause129]) ).
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_134,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause83,axiom,
! [VAR_0] :
( frontsegP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause83) ).
cnf(c_159,plain,
( frontsegP(nil,A)
| ~ ssList(A)
| nil != A ),
inference(clausify,[status(thm)],[clause83]) ).
fof(clause61,axiom,
! [VAR_0] :
( frontsegP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause61) ).
cnf(c_173,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause61]) ).
fof(clause60,axiom,
! [VAR_0] :
( frontsegP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause60) ).
cnf(c_174,plain,
( frontsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause60]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_226,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_21120,plain,
( sk3 = nil
| ~ frontsegP(sk1,sk3)
| ~ frontsegP(sk2,sk3)
| ~ ssList(sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_64,c_54]) ).
cnf(c_840,plain,
( sk3 = nil
| ~ frontsegP(sk1,sk3)
| ~ frontsegP(sk2,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_71,c_21120]) ).
cnf(c_21121,plain,
( sk3 = nil
| frontsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_97,c_52]) ).
cnf(c_21122,plain,
( sk3 = nil
| frontsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ frontsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_71,c_21121]) ).
cnf(c_925,plain,
( sk3 = nil
| frontsegP(A,sk3)
| ~ ssList(A)
| ~ frontsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_70,c_21122]) ).
cnf(c_21123,plain,
( sk4 = nil
| ~ ssList(sk3)
| ~ ssList(nil)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_134,c_58]) ).
cnf(c_21124,plain,
( sk4 = nil
| ~ ssList(sk3)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_226,c_21123]) ).
cnf(c_1061,plain,
( sk4 = nil
| sk3 != nil ),
inference(resolve,[status(thm)],[c_71,c_21124]) ).
cnf(c_21125,plain,
( frontsegP(nil,sk2)
| nil != sk2 ),
inference(resolve,[status(thm)],[c_159,c_72]) ).
cnf(c_1087,plain,
( frontsegP(nil,sk2)
| sk2 != nil ),
inference(copy,[status(thm)],[c_21125]) ).
cnf(c_1114,plain,
frontsegP(sk1,sk1),
inference(resolve,[status(thm)],[c_173,c_73]) ).
cnf(c_1117,plain,
frontsegP(sk4,sk4),
inference(resolve,[status(thm)],[c_173,c_70]) ).
cnf(c_1121,plain,
frontsegP(sk3,nil),
inference(resolve,[status(thm)],[c_174,c_71]) ).
cnf(c_4846,plain,
frontsegP(sk1,sk3),
inference(paramod,[status(thm)],[c_67,c_1114]) ).
cnf(c_4847,plain,
( sk3 = nil
| ~ frontsegP(sk2,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_4846,c_840]) ).
cnf(c_4866,plain,
frontsegP(sk2,sk4),
inference(paramod,[status(thm)],[c_69,c_1117]) ).
cnf(c_21126,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_1121,c_121]) ).
cnf(c_21127,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_226,c_21126]) ).
cnf(c_4988,plain,
( sk3 = nil
| ~ frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_71,c_21127]) ).
cnf(c_21128,plain,
( frontsegP(A,sk4)
| ~ ssList(A)
| ~ ssList(sk2)
| ~ ssList(sk4)
| ~ frontsegP(A,sk2) ),
inference(resolve,[status(thm)],[c_4866,c_97]) ).
cnf(c_21129,plain,
( frontsegP(A,sk4)
| ~ ssList(A)
| ~ ssList(sk2)
| ~ frontsegP(A,sk2) ),
inference(resolve,[status(thm)],[c_70,c_21128]) ).
cnf(c_5719,plain,
( frontsegP(A,sk4)
| ~ ssList(A)
| ~ frontsegP(A,sk2) ),
inference(resolve,[status(thm)],[c_72,c_21129]) ).
cnf(c_21130,plain,
( sk3 = nil
| frontsegP(sk2,sk3)
| ~ ssList(sk2) ),
inference(resolve,[status(thm)],[c_925,c_4866]) ).
cnf(c_11006,plain,
( sk3 = nil
| frontsegP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_72,c_21130]) ).
cnf(c_21131,plain,
( sk3 = nil
| sk3 = nil
| sk2 = nil ),
inference(resolve,[status(thm)],[c_4847,c_11006]) ).
cnf(c_20393,plain,
( sk3 = nil
| sk2 = nil ),
inference(copy,[status(thm)],[c_21131]) ).
cnf(c_20396,plain,
( frontsegP(nil,sk2)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_20393,c_1087]) ).
cnf(c_21132,plain,
( frontsegP(nil,sk4)
| ~ ssList(nil)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_20396,c_5719]) ).
cnf(c_20415,plain,
( frontsegP(nil,sk4)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_226,c_21132]) ).
cnf(c_21133,plain,
( sk3 = nil
| frontsegP(nil,sk3)
| ~ ssList(nil)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_20415,c_925]) ).
cnf(c_21134,plain,
( frontsegP(nil,sk3)
| ~ ssList(nil)
| sk3 = nil ),
inference(copy,[status(thm)],[c_21133]) ).
cnf(c_20472,plain,
( frontsegP(nil,sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_226,c_21134]) ).
cnf(c_21135,plain,
( sk3 = nil
| sk3 = nil ),
inference(resolve,[status(thm)],[c_20472,c_4988]) ).
cnf(c_20541,plain,
sk3 = nil,
inference(copy,[status(thm)],[c_21135]) ).
cnf(c_20598,plain,
sk4 = nil,
inference(resolve,[status(thm)],[c_20541,c_1061]) ).
cnf(c_20690,plain,
sk1 = nil,
inference(paramod,[status(thm)],[c_20541,c_67]) ).
cnf(c_20811,plain,
neq(sk2,nil),
inference(resolve,[status(thm)],[c_20690,c_62]) ).
cnf(c_21136,plain,
nil = sk2,
inference(paramod,[status(thm)],[c_20598,c_69]) ).
cnf(c_20868,plain,
sk2 = nil,
inference(copy,[status(thm)],[c_21136]) ).
cnf(c_21137,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_20811,c_134]) ).
cnf(c_21138,plain,
( ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_20868,c_21137]) ).
cnf(c_21139,plain,
~ ssList(sk2),
inference(resolve,[status(thm)],[c_226,c_21138]) ).
cnf(c_21119,plain,
$false,
inference(resolve,[status(thm)],[c_72,c_21139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC017-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.15/15.37 % CPULimit : 300
% 0.15/15.37 % WCLimit : 300
% 0.15/15.37 % DateTime : Sat Sep 26 12:09:16 UTC 2026
% 0.15/15.37 % CPUTime :
% 0.15/15.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/15.37 % Process 820717 was started by sandbox on n016,
% 0.15/15.37 % Sat Sep 26 12:09:16 2026
% 0.15/15.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/15.38
% 0.15/15.38 % From the command line: assign(max_seconds, 300).
% 26.71/20.47
% 26.71/20.47 % given #500 (I,wt=38): 564 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(304,c,f)].
% 26.71/20.47
% 26.71/20.47 % given #1000 (A,wt=20): 878 app(app(sk3,A),A) != B | -ssList(A) | -ssList(B) | segmentP(B,A). [factor(856,b,c)].
% 26.71/20.47
% 26.71/20.47 % given #1500 (T,wt=8): 12845 neq(sk3,sk4) | sk4 = sk3. [resolve(1073,a,71,a)].
% 26.71/20.47
% 26.71/20.47 % given #2000 (F,wt=13): 19267 cons(skaf59(A),skaf81(B)) != nil. [resolve(2090,b,220,a)].
% 26.71/20.47
% 26.71/20.47 % SZS status Unsatisfiable for theBenchmark
% 26.71/20.47
% 26.71/20.47 % Proof 1 at 2.54 (+ 0.82) seconds.
% 26.71/20.47 % Length of proof is 47.
% 26.71/20.47 % Level of proof is 11.
% 26.71/20.47 % Maximum clause weight is 17.000.
% 26.71/20.47 % Given clauses 2185.
% 26.71/20.47
% 26.71/20.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------