%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC241-1 : 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 : n017.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 211.83s 28.42s
% Output : CNFRefutation 211.83s
% 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_7930,plain,
nil != sk3,
inference(paramod,[status(thm)],[c_204,c_205]) ).
cnf(c_206,plain,
sk3 != nil,
inference(copy,[status(thm)],[c_7930]) ).
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_7931,plain,
( ssItem(sk6)
| sk3 = nil ),
inference(copy,[status(thm)],[c_217]) ).
cnf(c_218,plain,
ssItem(sk6),
inference(resolve,[status(thm)],[c_206,c_7931]) ).
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_7932,plain,
( ssList(sk7)
| sk3 = nil ),
inference(copy,[status(thm)],[c_219]) ).
cnf(c_220,plain,
ssList(sk7),
inference(resolve,[status(thm)],[c_206,c_7932]) ).
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_7933,plain,
( ssList(sk8)
| sk3 = nil ),
inference(copy,[status(thm)],[c_221]) ).
cnf(c_222,plain,
ssList(sk8),
inference(resolve,[status(thm)],[c_206,c_7933]) ).
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_7934,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_7934]) ).
cnf(c_4323,plain,
( leq(sk6,A)
| ~ ssItem(A)
| ~ lt(sk6,A) ),
inference(resolve,[status(thm)],[c_218,c_127]) ).
cnf(c_7935,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_216]) ).
cnf(c_7936,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_7935]) ).
cnf(c_7937,plain,
( ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_7936]) ).
cnf(c_4586,plain,
~ leq(sk6,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_222,c_7937]) ).
cnf(c_7938,plain,
( lt(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_214]) ).
cnf(c_7939,plain,
( lt(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_7938]) ).
cnf(c_7940,plain,
( lt(sk6,sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_7939]) ).
cnf(c_4587,plain,
lt(sk6,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_222,c_7940]) ).
cnf(c_7941,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_224,c_208]) ).
cnf(c_7942,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_218,c_7941]) ).
cnf(c_7943,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_220,c_7942]) ).
cnf(c_4590,plain,
ssItem(sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_222,c_7943]) ).
cnf(c_7944,plain,
( leq(sk6,sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(resolve,[status(thm)],[c_4590,c_4323]) ).
cnf(c_7945,plain,
leq(sk6,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_4587,c_7944]) ).
cnf(c_7929,plain,
$false,
inference(resolve,[status(thm)],[c_4586,c_7945]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC241-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n017.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 12:30:49 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 711581 was started by sandbox2 on n017,
% 0.18/0.43 % Sat Sep 26 12:30:49 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 211.83/28.42
% 211.83/28.42 % given #500 (I,wt=46): 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)].
% 211.83/28.42
% 211.83/28.42 % given #1000 (F,wt=15): 6201 -gt(hd(sk3),hd(sk3)). [resolve(4233,a,313,b)].
% 211.83/28.42
% 211.83/28.42 % SZS status Unsatisfiable for theBenchmark
% 211.83/28.42
% 211.83/28.42 % Proof 1 at 2.74 (+ 1.04) seconds.
% 211.83/28.42 % Length of proof is 23.
% 211.83/28.42 % Level of proof is 4.
% 211.83/28.42 % Maximum clause weight is 43.000.
% 211.83/28.42 % Given clauses 1346.
% 211.83/28.42
% 211.83/28.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------