%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC242-1 : 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 : 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 08:57:15 AM UTC 2026
% Result : Unsatisfiable 123.77s 33.41s
% Output : CNFRefutation 123.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 124 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 149 ( 74 ~; 75 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 6 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause103,axiom,
! [VAR_0,VAR_1] :
( leq(VAR_0,VAR_1)
| ~ ssItem(VAR_0)
| ~ ssItem(VAR_1)
| ~ lt(VAR_0,VAR_1) ),
file('theBenchmark.p',clause103) ).
cnf(c_127,plain,
( leq(A,B)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ lt(A,B) ),
inference(clausify,[status(thm)],[clause103]) ).
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_7912,plain,
nil != sk3,
inference(paramod,[status(thm)],[c_204,c_205]) ).
cnf(c_206,plain,
sk3 != nil,
inference(copy,[status(thm)],[c_7912]) ).
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_11,axiom,
! [VAR_0,VAR_1,VAR_2] :
( lt(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,
( lt(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,
( lt(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(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_12) ).
cnf(c_215,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_12]) ).
cnf(c_216,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_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_7913,plain,
( ssItem(sk6)
| sk3 = nil ),
inference(copy,[status(thm)],[c_217]) ).
cnf(c_218,plain,
ssItem(sk6),
inference(resolve,[status(thm)],[c_206,c_7913]) ).
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_7914,plain,
( ssList(sk7)
| sk3 = nil ),
inference(copy,[status(thm)],[c_219]) ).
cnf(c_220,plain,
ssList(sk7),
inference(resolve,[status(thm)],[c_206,c_7914]) ).
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_7915,plain,
( ssList(sk8)
| sk3 = nil ),
inference(copy,[status(thm)],[c_221]) ).
cnf(c_222,plain,
ssList(sk8),
inference(resolve,[status(thm)],[c_206,c_7915]) ).
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_7916,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_7916]) ).
cnf(c_4323,plain,
( leq(sk6,A)
| ~ ssItem(A)
| ~ lt(sk6,A) ),
inference(resolve,[status(thm)],[c_218,c_127]) ).
cnf(c_7917,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_216]) ).
cnf(c_7918,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_7917]) ).
cnf(c_7919,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_7918]) ).
cnf(c_4586,plain,
~ leq(sk6,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_222,c_7919]) ).
cnf(c_7920,plain,
( lt(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_214]) ).
cnf(c_7921,plain,
( lt(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_7920]) ).
cnf(c_7922,plain,
( lt(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_7921]) ).
cnf(c_4587,plain,
lt(sk6,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_222,c_7922]) ).
cnf(c_7923,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_208]) ).
cnf(c_7924,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_7923]) ).
cnf(c_7925,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_7924]) ).
cnf(c_4590,plain,
ssItem(sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_222,c_7925]) ).
cnf(c_7926,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(resolve,[status(thm)],[c_4590,c_4323]) ).
cnf(c_7927,plain,
leq(sk6,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_4587,c_7926]) ).
cnf(c_7911,plain,
$false,
inference(resolve,[status(thm)],[c_4586,c_7927]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC242-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.44 % Computer : n010.cluster.edu
% 0.08/5.44 % Model : x86_64 x86_64
% 0.08/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.44 % Memory : 8046.5625MB
% 0.08/5.44 % OS : Linux 6.8.0-71-generic
% 0.08/5.45 % CPULimit : 300
% 0.08/5.45 % WCLimit : 300
% 0.08/5.45 % DateTime : Sat Sep 26 12:36:06 UTC 2026
% 0.08/5.45 % CPUTime :
% 0.08/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.45 % Process 3312822 was started by sandbox on n010,
% 0.08/5.45 % Sat Sep 26 12:36:06 2026
% 0.08/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.46
% 0.08/5.46 % From the command line: assign(max_seconds, 300).
% 123.77/33.41
% 123.77/33.41 % given #500 (I,wt=46): 567 app(app(A,cons(B,A)),cons(C,D)) != A | -ssList(D) | -ssList(A) | -ssItem(C) | -ssItem(B) | -totalorderedP(A) | leq(B,C). [factor(373,c,g)].
% 123.77/33.41
% 123.77/33.41 % given #1000 (T,wt=11): 6608 -frontsegP(nil,sk8) | frontsegP(sk3,sk8). [resolve(5503,b,222,a)].
% 123.77/33.41
% 123.77/33.41 % SZS status Unsatisfiable for theBenchmark
% 123.77/33.41
% 123.77/33.41 % Proof 1 at 2.73 (+ 1.04) seconds.
% 123.77/33.41 % Length of proof is 23.
% 123.77/33.41 % Level of proof is 4.
% 123.77/33.41 % Maximum clause weight is 43.000.
% 123.77/33.41 % Given clauses 1345.
% 123.77/33.41
% 123.77/33.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------