%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC004-1 : 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 : n003.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 08:56:30 AM UTC 2026
% Result : Unsatisfiable 114.68s 16.09s
% Output : CNFRefutation 114.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 18 unt; 0 def)
% Number of atoms : 141 ( 37 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 173 ( 90 ~; 83 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_20,axiom,
( ~ neq(sk4,nil)
| app(sk6,sk7) = sk3 ),
file('theBenchmark.p',co1_20) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| app(sk6,sk7) = sk3 ),
inference(clausify,[status(thm)],[co1_20]) ).
fof(co1_19,axiom,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
file('theBenchmark.p',co1_19) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
inference(clausify,[status(thm)],[co1_19]) ).
fof(co1_18,axiom,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('theBenchmark.p',co1_18) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| ssList(sk7) ),
inference(clausify,[status(thm)],[co1_18]) ).
fof(co1_17,axiom,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('theBenchmark.p',co1_17) ).
cnf(c_54,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_17]) ).
fof(co1_16,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_16) ).
cnf(c_55,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_16]) ).
fof(co1_15,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ neq(sk4,nil)
| ~ neq(VAR_1,nil)
| app(VAR_0,VAR_2) != sk1
| app(app(VAR_0,VAR_1),VAR_2) != sk2
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_15) ).
cnf(c_56,plain,
( ~ neq(sk4,nil)
| ~ neq(B,nil)
| app(A,C) != sk1
| app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_15]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_64,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_65,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_64]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_66,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_67,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_68,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_67]) ).
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_148,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause98,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,VAR_1) != nil ),
file('theBenchmark.p',clause98) ).
cnf(c_150,plain,
( ~ ssList(B)
| ~ ssItem(A)
| cons(A,B) != nil ),
inference(clausify,[status(thm)],[clause98]) ).
fof(clause86,axiom,
! [VAR_0,VAR_1] :
( ssList(cons(VAR_0,VAR_1))
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',clause86) ).
cnf(c_155,plain,
( ssList(cons(A,B))
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[clause86]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_225,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_30707,plain,
( ~ neq(sk4,nil)
| ~ neq(B,nil)
| app(A,C) != sk3
| app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_66,c_56]) ).
cnf(c_30708,plain,
( ~ neq(sk2,nil)
| ~ neq(B,nil)
| app(A,C) != sk3
| app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_68,c_30707]) ).
cnf(c_333,plain,
( ~ neq(B,nil)
| app(A,C) != sk3
| app(app(A,B),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_65,c_30708]) ).
cnf(c_30709,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_68,c_55]) ).
cnf(c_334,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_65,c_30709]) ).
cnf(c_30710,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(paramod,[status(thm)],[c_68,c_54]) ).
cnf(c_335,plain,
ssList(sk6),
inference(resolve,[status(thm)],[c_65,c_30710]) ).
cnf(c_30711,plain,
( ~ neq(sk2,nil)
| ssList(sk7) ),
inference(paramod,[status(thm)],[c_68,c_53]) ).
cnf(c_336,plain,
ssList(sk7),
inference(resolve,[status(thm)],[c_65,c_30711]) ).
cnf(c_30712,plain,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk2 ),
inference(paramod,[status(thm)],[c_68,c_52]) ).
cnf(c_30713,plain,
( ~ neq(sk2,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk2 ),
inference(paramod,[status(thm)],[c_68,c_30712]) ).
cnf(c_337,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk2,
inference(resolve,[status(thm)],[c_65,c_30713]) ).
cnf(c_30714,plain,
( ~ neq(sk2,nil)
| app(sk6,sk7) = sk3 ),
inference(paramod,[status(thm)],[c_68,c_51]) ).
cnf(c_338,plain,
app(sk6,sk7) = sk3,
inference(resolve,[status(thm)],[c_65,c_30714]) ).
cnf(c_7417,plain,
( ssList(cons(A,nil))
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_225,c_155]) ).
cnf(c_7420,plain,
( ~ ssItem(A)
| cons(A,nil) != nil ),
inference(resolve,[status(thm)],[c_225,c_150]) ).
cnf(c_30715,plain,
( A = nil
| neq(A,nil)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_225,c_148]) ).
cnf(c_7422,plain,
( nil = A
| neq(A,nil)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_30715]) ).
cnf(c_30716,plain,
( ~ neq(cons(sk5,nil),nil)
| app(sk6,sk7) != sk3
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_337,c_333]) ).
cnf(c_30717,plain,
( ~ neq(cons(sk5,nil),nil)
| sk3 != sk3
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(paramod,[status(thm)],[c_338,c_30716]) ).
cnf(c_30718,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(copy,[status(thm)],[c_30717]) ).
cnf(c_30719,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil)) ),
inference(resolve,[status(thm)],[c_335,c_30718]) ).
cnf(c_8568,plain,
( ~ neq(cons(sk5,nil),nil)
| ~ ssList(cons(sk5,nil)) ),
inference(resolve,[status(thm)],[c_336,c_30719]) ).
cnf(c_15835,plain,
cons(sk5,nil) != nil,
inference(resolve,[status(thm)],[c_7420,c_334]) ).
cnf(c_28387,plain,
ssList(cons(sk5,nil)),
inference(resolve,[status(thm)],[c_7417,c_334]) ).
cnf(c_28409,plain,
~ neq(cons(sk5,nil),nil),
inference(resolve,[status(thm)],[c_28387,c_8568]) ).
cnf(c_30720,plain,
( nil = cons(sk5,nil)
| neq(cons(sk5,nil),nil) ),
inference(resolve,[status(thm)],[c_7422,c_28387]) ).
cnf(c_30721,plain,
( cons(sk5,nil) = nil
| neq(cons(sk5,nil),nil) ),
inference(copy,[status(thm)],[c_30720]) ).
cnf(c_30722,plain,
cons(sk5,nil) = nil,
inference(resolve,[status(thm)],[c_28409,c_30721]) ).
cnf(c_30706,plain,
$false,
inference(resolve,[status(thm)],[c_15835,c_30722]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC004-1 : 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 : n003.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
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 12:04:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2817156 was started by sandbox on n003,
% 0.11/0.38 % Sat Sep 26 12:04:26 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 114.68/16.09
% 114.68/16.09 % given #500 (I,wt=40): 571 app(app(A,cons(B,A)),cons(C,D)) != D | -ssList(D) | -ssList(A) | -ssItem(C) | -ssItem(B) | lt(B,C) | lt(C,B) | -lt(skaf59(D),skaf60(D)). [factor(302,c,d)].
% 114.68/16.09
% 114.68/16.09 % given #1000 (T,wt=8): 7231 strictorderedP(cons(skac2,nil)). [resolve(223,a,169,a)].
% 114.68/16.09
% 114.68/16.09 % given #1500 (F,wt=12): 13717 skaf81(A) != sk3 | -neq(skaf81(A),sk3). [resolve(1154,c,219,a),flip(a)].
% 114.68/16.09
% 114.68/16.09 % given #2000 (T,wt=9): 22469 neq(sk2,cons(skac2,sk2)). [resolve(22258,a,1180,a),flip(b),unit_del(b,15319)].
% 114.68/16.09
% 114.68/16.09 % given #2500 (F,wt=12): 14284 skaf65(A) != skac3 | -lt(skaf65(A),skac3). [resolve(7346,c,203,a),flip(a)].
% 114.68/16.09
% 114.68/16.09 % SZS status Unsatisfiable for theBenchmark
% 114.68/16.09
% 114.68/16.09 % Proof 1 at 5.47 (+ 1.76) seconds.
% 114.68/16.09 % Length of proof is 29.
% 114.68/16.09 % Level of proof is 5.
% 114.68/16.09 % Maximum clause weight is 32.000.
% 114.68/16.09 % Given clauses 2879.
% 114.68/16.09
% 114.68/16.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------