%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC048-1 : 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 : n010.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 08:56:40 AM UTC 2026
% Result : Unsatisfiable 34.75s 5.45s
% Output : CNFRefutation 34.75s
% 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,
( rearsegP(sk4,sk3)
| nil = sk3 ),
file('theBenchmark.p',co1_14) ).
cnf(c_51,plain,
( rearsegP(sk4,sk3)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_52,plain,
( rearsegP(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] :
( ~ rearsegP(sk1,VAR_0)
| ~ rearsegP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sk2 ),
file('theBenchmark.p',co1_8) ).
cnf(c_63,plain,
( ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_64,plain,
( ~ rearsegP(sk1,A)
| ~ rearsegP(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(clause153,axiom,
! [VAR_0,VAR_1,VAR_2] :
( rearsegP(VAR_0,VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_2)
| ~ rearsegP(VAR_1,VAR_2)
| ~ rearsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause153) ).
cnf(c_98,plain,
( rearsegP(A,C)
| ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ~ rearsegP(B,C)
| ~ rearsegP(A,B) ),
inference(clausify,[status(thm)],[clause153]) ).
fof(clause128,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ rearsegP(VAR_1,VAR_0)
| ~ rearsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause128) ).
cnf(c_122,plain,
( B = A
| ~ ssList(B)
| ~ ssList(A)
| ~ rearsegP(B,A)
| ~ rearsegP(A,B) ),
inference(clausify,[status(thm)],[clause128]) ).
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(clause81,axiom,
! [VAR_0] :
( rearsegP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause81) ).
cnf(c_161,plain,
( rearsegP(nil,A)
| ~ ssList(A)
| nil != A ),
inference(clausify,[status(thm)],[clause81]) ).
fof(clause59,axiom,
! [VAR_0] :
( rearsegP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause59) ).
cnf(c_175,plain,
( rearsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause59]) ).
fof(clause58,axiom,
! [VAR_0] :
( rearsegP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause58) ).
cnf(c_176,plain,
( rearsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause58]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_226,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_21884,plain,
( sk3 = nil
| ~ rearsegP(sk1,sk3)
| ~ rearsegP(sk2,sk3)
| ~ ssList(sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_64,c_54]) ).
cnf(c_840,plain,
( sk3 = nil
| ~ rearsegP(sk1,sk3)
| ~ rearsegP(sk2,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_71,c_21884]) ).
cnf(c_21885,plain,
( sk3 = nil
| rearsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ rearsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_98,c_52]) ).
cnf(c_21886,plain,
( sk3 = nil
| rearsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ rearsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_71,c_21885]) ).
cnf(c_921,plain,
( sk3 = nil
| rearsegP(A,sk3)
| ~ ssList(A)
| ~ rearsegP(A,sk4) ),
inference(resolve,[status(thm)],[c_70,c_21886]) ).
cnf(c_21887,plain,
( sk4 = nil
| ~ ssList(sk3)
| ~ ssList(nil)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_134,c_58]) ).
cnf(c_21888,plain,
( sk4 = nil
| ~ ssList(sk3)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_226,c_21887]) ).
cnf(c_1057,plain,
( sk4 = nil
| sk3 != nil ),
inference(resolve,[status(thm)],[c_71,c_21888]) ).
cnf(c_21889,plain,
( rearsegP(nil,sk2)
| nil != sk2 ),
inference(resolve,[status(thm)],[c_161,c_72]) ).
cnf(c_1087,plain,
( rearsegP(nil,sk2)
| sk2 != nil ),
inference(copy,[status(thm)],[c_21889]) ).
cnf(c_1118,plain,
rearsegP(sk1,sk1),
inference(resolve,[status(thm)],[c_175,c_73]) ).
cnf(c_1121,plain,
rearsegP(sk4,sk4),
inference(resolve,[status(thm)],[c_175,c_70]) ).
cnf(c_1125,plain,
rearsegP(sk3,nil),
inference(resolve,[status(thm)],[c_176,c_71]) ).
cnf(c_4929,plain,
rearsegP(sk1,sk3),
inference(paramod,[status(thm)],[c_67,c_1118]) ).
cnf(c_4930,plain,
( sk3 = nil
| ~ rearsegP(sk2,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_4929,c_840]) ).
cnf(c_4943,plain,
rearsegP(sk2,sk4),
inference(paramod,[status(thm)],[c_69,c_1121]) ).
cnf(c_21890,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ rearsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_1125,c_122]) ).
cnf(c_21891,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ rearsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_226,c_21890]) ).
cnf(c_5006,plain,
( sk3 = nil
| ~ rearsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_71,c_21891]) ).
cnf(c_21892,plain,
( rearsegP(A,sk4)
| ~ ssList(A)
| ~ ssList(sk2)
| ~ ssList(sk4)
| ~ rearsegP(A,sk2) ),
inference(resolve,[status(thm)],[c_4943,c_98]) ).
cnf(c_21893,plain,
( rearsegP(A,sk4)
| ~ ssList(A)
| ~ ssList(sk2)
| ~ rearsegP(A,sk2) ),
inference(resolve,[status(thm)],[c_70,c_21892]) ).
cnf(c_6248,plain,
( rearsegP(A,sk4)
| ~ ssList(A)
| ~ rearsegP(A,sk2) ),
inference(resolve,[status(thm)],[c_72,c_21893]) ).
cnf(c_21894,plain,
( sk3 = nil
| rearsegP(sk2,sk3)
| ~ ssList(sk2) ),
inference(resolve,[status(thm)],[c_921,c_4943]) ).
cnf(c_10922,plain,
( sk3 = nil
| rearsegP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_72,c_21894]) ).
cnf(c_21895,plain,
( sk3 = nil
| sk3 = nil
| sk2 = nil ),
inference(resolve,[status(thm)],[c_4930,c_10922]) ).
cnf(c_21183,plain,
( sk3 = nil
| sk2 = nil ),
inference(copy,[status(thm)],[c_21895]) ).
cnf(c_21185,plain,
( rearsegP(nil,sk2)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_21183,c_1087]) ).
cnf(c_21896,plain,
( rearsegP(nil,sk4)
| ~ ssList(nil)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_21185,c_6248]) ).
cnf(c_21196,plain,
( rearsegP(nil,sk4)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_226,c_21896]) ).
cnf(c_21897,plain,
( sk3 = nil
| rearsegP(nil,sk3)
| ~ ssList(nil)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_21196,c_921]) ).
cnf(c_21898,plain,
( rearsegP(nil,sk3)
| ~ ssList(nil)
| sk3 = nil ),
inference(copy,[status(thm)],[c_21897]) ).
cnf(c_21261,plain,
( rearsegP(nil,sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_226,c_21898]) ).
cnf(c_21899,plain,
( sk3 = nil
| sk3 = nil ),
inference(resolve,[status(thm)],[c_21261,c_5006]) ).
cnf(c_21356,plain,
sk3 = nil,
inference(copy,[status(thm)],[c_21899]) ).
cnf(c_21413,plain,
sk4 = nil,
inference(resolve,[status(thm)],[c_21356,c_1057]) ).
cnf(c_21505,plain,
sk1 = nil,
inference(paramod,[status(thm)],[c_21356,c_67]) ).
cnf(c_21628,plain,
neq(sk2,nil),
inference(resolve,[status(thm)],[c_21505,c_62]) ).
cnf(c_21900,plain,
nil = sk2,
inference(paramod,[status(thm)],[c_21413,c_69]) ).
cnf(c_21684,plain,
sk2 = nil,
inference(copy,[status(thm)],[c_21900]) ).
cnf(c_21901,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_21628,c_134]) ).
cnf(c_21902,plain,
( ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_21684,c_21901]) ).
cnf(c_21903,plain,
~ ssList(sk2),
inference(resolve,[status(thm)],[c_226,c_21902]) ).
cnf(c_21883,plain,
$false,
inference(resolve,[status(thm)],[c_72,c_21903]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC048-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n010.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 12:08:15 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 3252283 was started by sandbox2 on n010,
% 0.11/0.37 % Sat Sep 26 12:08:15 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 34.75/5.45
% 34.75/5.45 % 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)].
% 34.75/5.45
% 34.75/5.45 % given #1000 (A,wt=20): 876 app(app(sk4,A),A) != B | -ssList(A) | -ssList(B) | segmentP(B,A). [factor(853,b,c)].
% 34.75/5.45
% 34.75/5.45 % given #1500 (T,wt=8): 12780 neq(sk3,sk4) | sk4 = sk3. [resolve(1069,a,71,a)].
% 34.75/5.45
% 34.75/5.45 % given #2000 (F,wt=13): 19219 cons(skaf59(A),skaf81(B)) != nil. [resolve(2086,b,220,a)].
% 34.75/5.45
% 34.75/5.45 % SZS status Unsatisfiable for theBenchmark
% 34.75/5.45
% 34.75/5.45 % Proof 1 at 3.64 (+ 1.36) seconds.
% 34.75/5.45 % Length of proof is 47.
% 34.75/5.45 % Level of proof is 11.
% 34.75/5.45 % Maximum clause weight is 17.000.
% 34.75/5.45 % Given clauses 2245.
% 34.75/5.45
% 34.75/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------