%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC220-1 : 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 : n014.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 08:57:12 AM UTC 2026
% Result : Unsatisfiable 28.53s 4.54s
% Output : CNFRefutation 28.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 17 unt; 0 def)
% Number of atoms : 193 ( 40 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 253 ( 126 ~; 127 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 49 ( 0 sgn 16 !; 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,
nil != sk1,
file('theBenchmark.p',co1_7) ).
cnf(c_205,plain,
nil != sk1,
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_12333,plain,
nil != sk3,
inference(paramod,[status(thm)],[c_204,c_205]) ).
cnf(c_206,plain,
sk3 != nil,
inference(copy,[status(thm)],[c_12333]) ).
fof(co1_8,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ssItem(sk5(VAR_2,VAR_1,VAR_0))
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk1
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_207,plain,
( ssItem(sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_208,plain,
( ssItem(sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_204,c_207]) ).
fof(co1_9,axiom,
! [VAR_0,VAR_1,VAR_2] :
( memberP(VAR_1,sk5(VAR_2,VAR_1,VAR_0))
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk1
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_9) ).
cnf(c_209,plain,
( memberP(B,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_210,plain,
( memberP(B,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_204,c_209]) ).
fof(co1_10,axiom,
! [VAR_0,VAR_1,VAR_2] :
( memberP(VAR_2,sk5(VAR_2,VAR_1,VAR_0))
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk1
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_10) ).
cnf(c_211,plain,
( memberP(C,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_212,plain,
( memberP(C,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_204,c_211]) ).
fof(co1_11,axiom,
! [VAR_0,VAR_1,VAR_2] :
( leq(VAR_0,sk5(VAR_2,VAR_1,VAR_0))
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk1
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_11) ).
cnf(c_213,plain,
( leq(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_214,plain,
( leq(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_204,c_213]) ).
fof(co1_12,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ leq(sk5(VAR_2,VAR_1,VAR_0),VAR_0)
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk1
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_12) ).
cnf(c_215,plain,
( ~ leq(sk5(C,B,A),A)
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_216,plain,
( ~ leq(sk5(C,B,A),A)
| app(app(B,cons(A,nil)),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_204,c_215]) ).
fof(co1_13,axiom,
( ssItem(sk6)
| nil = sk3 ),
file('theBenchmark.p',co1_13) ).
cnf(c_217,plain,
( ssItem(sk6)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_12334,plain,
( ssItem(sk6)
| sk3 = nil ),
inference(copy,[status(thm)],[c_217]) ).
cnf(c_218,plain,
ssItem(sk6),
inference(resolve,[status(thm)],[c_206,c_12334]) ).
fof(co1_14,axiom,
( ssList(sk7)
| nil = sk3 ),
file('theBenchmark.p',co1_14) ).
cnf(c_219,plain,
( ssList(sk7)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_12335,plain,
( ssList(sk7)
| sk3 = nil ),
inference(copy,[status(thm)],[c_219]) ).
cnf(c_220,plain,
ssList(sk7),
inference(resolve,[status(thm)],[c_206,c_12335]) ).
fof(co1_15,axiom,
( ssList(sk8)
| nil = sk3 ),
file('theBenchmark.p',co1_15) ).
cnf(c_221,plain,
( ssList(sk8)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_15]) ).
cnf(c_12336,plain,
( ssList(sk8)
| sk3 = nil ),
inference(copy,[status(thm)],[c_221]) ).
cnf(c_222,plain,
ssList(sk8),
inference(resolve,[status(thm)],[c_206,c_12336]) ).
fof(co1_16,axiom,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk3 ),
file('theBenchmark.p',co1_16) ).
cnf(c_223,plain,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_16]) ).
cnf(c_12337,plain,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| sk3 = nil ),
inference(copy,[status(thm)],[c_223]) ).
cnf(c_224,plain,
app(app(sk7,cons(sk6,nil)),sk8) = sk3,
inference(resolve,[status(thm)],[c_206,c_12337]) ).
fof(co1_17,axiom,
! [VAR_0] :
( ~ leq(sk6,VAR_0)
| ~ memberP(sk8,VAR_0)
| ~ memberP(sk7,VAR_0)
| leq(VAR_0,sk6)
| ~ ssItem(VAR_0)
| nil = sk3 ),
file('theBenchmark.p',co1_17) ).
cnf(c_225,plain,
( ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6)
| ~ ssItem(A)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_17]) ).
cnf(c_12338,plain,
( ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6)
| ~ ssItem(A)
| sk3 = nil ),
inference(copy,[status(thm)],[c_225]) ).
cnf(c_226,plain,
( ~ leq(sk6,A)
| ~ memberP(sk8,A)
| ~ memberP(sk7,A)
| leq(A,sk6)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_206,c_12338]) ).
cnf(c_12339,plain,
( ~ leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_216]) ).
cnf(c_12340,plain,
( ~ leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_12339]) ).
cnf(c_12341,plain,
( ~ leq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_12340]) ).
cnf(c_7868,plain,
~ leq(sk5(sk8,sk7,sk6),sk6),
inference(resolve,[status(thm)],[c_222,c_12341]) ).
cnf(c_12342,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_214]) ).
cnf(c_12343,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_12342]) ).
cnf(c_12344,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_12343]) ).
cnf(c_7869,plain,
leq(sk6,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_222,c_12344]) ).
cnf(c_12345,plain,
( memberP(sk8,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_212]) ).
cnf(c_12346,plain,
( memberP(sk8,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_12345]) ).
cnf(c_12347,plain,
( memberP(sk8,sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_12346]) ).
cnf(c_7870,plain,
memberP(sk8,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_222,c_12347]) ).
cnf(c_12348,plain,
( memberP(sk7,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_210]) ).
cnf(c_12349,plain,
( memberP(sk7,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_12348]) ).
cnf(c_12350,plain,
( memberP(sk7,sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_12349]) ).
cnf(c_7871,plain,
memberP(sk7,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_222,c_12350]) ).
cnf(c_12351,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_208]) ).
cnf(c_12352,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_12351]) ).
cnf(c_12353,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_12352]) ).
cnf(c_7872,plain,
ssItem(sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_222,c_12353]) ).
cnf(c_12354,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6))
| leq(sk5(sk8,sk7,sk6),sk6) ),
inference(resolve,[status(thm)],[c_7872,c_226]) ).
cnf(c_12355,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6)) ),
inference(resolve,[status(thm)],[c_7868,c_12354]) ).
cnf(c_12356,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ memberP(sk8,sk5(sk8,sk7,sk6)) ),
inference(resolve,[status(thm)],[c_7871,c_12355]) ).
cnf(c_12357,plain,
~ leq(sk6,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_7870,c_12356]) ).
cnf(c_12332,plain,
$false,
inference(resolve,[status(thm)],[c_7869,c_12357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC220-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 12:32:16 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3156619 was started by sandbox on n014,
% 0.09/0.35 % Sat Sep 26 12:32:16 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 28.53/4.54
% 28.53/4.54 % given #500 (I,wt=34): 566 app(app(A,cons(B,A)),cons(C,D)) != D | -ssList(D) | -ssList(A) | -ssItem(C) | -ssItem(B) | -totalorderedP(D) | leq(B,C). [factor(372,c,d)].
% 28.53/4.54
% 28.53/4.54 % given #1000 (F,wt=8): 11379 -leq(sk6,skac3) | -lt(skac3,sk6). [resolve(9209,c,50,a)].
% 28.53/4.54
% 28.53/4.54 % SZS status Unsatisfiable for theBenchmark
% 28.53/4.54
% 28.53/4.54 % Proof 1 at 3.11 (+ 0.98) seconds.
% 28.53/4.54 % Length of proof is 29.
% 28.53/4.54 % Level of proof is 4.
% 28.53/4.54 % Maximum clause weight is 31.000.
% 28.53/4.54 % Given clauses 1201.
% 28.53/4.54
% 28.53/4.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------