%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC279-1 : 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 : n013.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 08:57:22 AM UTC 2026
% Result : Unsatisfiable 221.30s 29.68s
% Output : CNFRefutation 221.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 18 unt; 0 def)
% Number of atoms : 113 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 133 ( 65 ~; 68 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_204,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_7,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ memberP(VAR_2,VAR_3)
| leq(VAR_0,VAR_3)
| ~ ssItem(VAR_3)
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk3
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_205,plain,
( ~ memberP(C,D)
| leq(A,D)
| ~ ssItem(D)
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ memberP(VAR_1,VAR_3)
| leq(VAR_3,VAR_0)
| ~ ssItem(VAR_3)
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk3
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_206,plain,
( ~ memberP(B,D)
| leq(D,A)
| ~ ssItem(D)
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_9,axiom,
ssItem(sk5),
file('theBenchmark.p',co1_9) ).
cnf(c_207,plain,
ssItem(sk5),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_10,axiom,
ssList(sk6),
file('theBenchmark.p',co1_10) ).
cnf(c_208,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_11,axiom,
ssList(sk7),
file('theBenchmark.p',co1_11) ).
cnf(c_209,plain,
ssList(sk7),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_12,axiom,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('theBenchmark.p',co1_12) ).
cnf(c_210,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_211,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk3,
inference(paramod,[status(thm)],[c_204,c_210]) ).
fof(co1_13,axiom,
ssItem(sk8),
file('theBenchmark.p',co1_13) ).
cnf(c_212,plain,
ssItem(sk8),
inference(clausify,[status(thm)],[co1_13]) ).
fof(co1_14,axiom,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
file('theBenchmark.p',co1_14) ).
cnf(c_213,plain,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
inference(clausify,[status(thm)],[co1_14]) ).
fof(co1_15,axiom,
( ~ leq(sk5,sk8)
| memberP(sk6,sk8) ),
file('theBenchmark.p',co1_15) ).
cnf(c_214,plain,
( ~ leq(sk5,sk8)
| memberP(sk6,sk8) ),
inference(clausify,[status(thm)],[co1_15]) ).
fof(co1_16,axiom,
( memberP(sk7,sk8)
| ~ leq(sk8,sk5) ),
file('theBenchmark.p',co1_16) ).
cnf(c_215,plain,
( memberP(sk7,sk8)
| ~ leq(sk8,sk5) ),
inference(clausify,[status(thm)],[co1_16]) ).
fof(co1_17,axiom,
( ~ leq(sk5,sk8)
| ~ leq(sk8,sk5) ),
file('theBenchmark.p',co1_17) ).
cnf(c_216,plain,
( ~ leq(sk5,sk8)
| ~ leq(sk8,sk5) ),
inference(clausify,[status(thm)],[co1_17]) ).
cnf(c_6630,plain,
( ~ memberP(sk6,A)
| leq(A,sk5)
| ~ ssItem(A)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_211,c_206]) ).
cnf(c_6631,plain,
( ~ memberP(sk6,A)
| leq(A,sk5)
| ~ ssItem(A)
| ~ ssList(sk7)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_207,c_6630]) ).
cnf(c_6632,plain,
( ~ memberP(sk6,A)
| leq(A,sk5)
| ~ ssItem(A)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_208,c_6631]) ).
cnf(c_4581,plain,
( ~ memberP(sk6,A)
| leq(A,sk5)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_209,c_6632]) ).
cnf(c_6633,plain,
( ~ memberP(sk7,A)
| leq(sk5,A)
| ~ ssItem(A)
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_211,c_205]) ).
cnf(c_6634,plain,
( ~ memberP(sk7,A)
| leq(sk5,A)
| ~ ssItem(A)
| ~ ssList(sk7)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_207,c_6633]) ).
cnf(c_6635,plain,
( ~ memberP(sk7,A)
| leq(sk5,A)
| ~ ssItem(A)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_208,c_6634]) ).
cnf(c_4582,plain,
( ~ memberP(sk7,A)
| leq(sk5,A)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_209,c_6635]) ).
cnf(c_6530,plain,
( ~ memberP(sk6,sk8)
| leq(sk8,sk5) ),
inference(resolve,[status(thm)],[c_4581,c_212]) ).
cnf(c_6548,plain,
( ~ memberP(sk7,sk8)
| leq(sk5,sk8) ),
inference(resolve,[status(thm)],[c_4582,c_212]) ).
cnf(c_6636,plain,
( memberP(sk6,sk8)
| leq(sk5,sk8)
| ~ ssItem(sk8) ),
inference(resolve,[status(thm)],[c_4582,c_213]) ).
cnf(c_6566,plain,
( memberP(sk6,sk8)
| leq(sk5,sk8) ),
inference(resolve,[status(thm)],[c_212,c_6636]) ).
cnf(c_6570,plain,
( leq(sk8,sk5)
| leq(sk5,sk8) ),
inference(resolve,[status(thm)],[c_6566,c_6530]) ).
cnf(c_6576,plain,
( memberP(sk6,sk8)
| leq(sk8,sk5) ),
inference(resolve,[status(thm)],[c_6570,c_214]) ).
cnf(c_6637,plain,
( leq(sk8,sk5)
| leq(sk8,sk5) ),
inference(resolve,[status(thm)],[c_6576,c_6530]) ).
cnf(c_6618,plain,
leq(sk8,sk5),
inference(copy,[status(thm)],[c_6637]) ).
cnf(c_6621,plain,
~ leq(sk5,sk8),
inference(resolve,[status(thm)],[c_6618,c_216]) ).
cnf(c_6622,plain,
memberP(sk7,sk8),
inference(resolve,[status(thm)],[c_6618,c_215]) ).
cnf(c_6638,plain,
~ memberP(sk7,sk8),
inference(resolve,[status(thm)],[c_6621,c_6548]) ).
cnf(c_6629,plain,
$false,
inference(resolve,[status(thm)],[c_6622,c_6638]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC279-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n013.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 12:40:06 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2763454 was started by sandbox on n013,
% 0.16/0.43 % Sat Sep 26 12:40:06 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 221.30/29.68
% 221.30/29.68 % given #500 (I,wt=60): 556 app(A,cons(B,cons(C,A))) != A | -ssList(A) | -ssItem(C) | -ssItem(B) | B = C | app(skaf80(A),cons(skaf78(A),cons(skaf79(A),skaf81(A)))) = A. [factor(368,b,e)].
% 221.30/29.68
% 221.30/29.68 % given #1000 (T,wt=11): 6322 -leq(sk5,skac2) | geq(skac2,sk5). [resolve(1853,b,207,a)].
% 221.30/29.68
% 221.30/29.68 % SZS status Unsatisfiable for theBenchmark
% 221.30/29.68
% 221.30/29.68 % Proof 1 at 3.56 (+ 1.33) seconds.
% 221.30/29.68 % Length of proof is 24.
% 221.30/29.68 % Level of proof is 8.
% 221.30/29.68 % Maximum clause weight is 45.000.
% 221.30/29.68 % Given clauses 1065.
% 221.30/29.68
% 221.30/29.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------