%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC096-1 : 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 : n001.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 08:56:48 AM UTC 2026
% Result : Unsatisfiable 23.06s 3.38s
% Output : CNFRefutation 23.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 80 ( 34 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 93 ( 51 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_18,axiom,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
file('theBenchmark.p',co1_18) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(clausify,[status(thm)],[co1_18]) ).
fof(co1_17,axiom,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_17) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_17]) ).
fof(co1_16,axiom,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('theBenchmark.p',co1_16) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_16]) ).
fof(co1_15,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_15) ).
cnf(c_54,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_15]) ).
fof(co1_14,axiom,
! [VAR_0,VAR_1] :
( ~ neq(sk4,nil)
| app(VAR_1,cons(VAR_0,nil)) != sk2
| cons(VAR_0,nil) != sk1
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_14) ).
cnf(c_55,plain,
( ~ neq(sk4,nil)
| app(B,cons(A,nil)) != sk2
| cons(A,nil) != sk1
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_14]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_62,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_63,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_62]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_64,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_65,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_66,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_65]) ).
cnf(c_15535,plain,
( ~ neq(sk4,nil)
| app(B,cons(A,nil)) != sk2
| cons(A,nil) != sk3
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_64,c_55]) ).
cnf(c_15536,plain,
( ~ neq(sk2,nil)
| app(B,cons(A,nil)) != sk2
| cons(A,nil) != sk3
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_66,c_15535]) ).
cnf(c_327,plain,
( app(B,cons(A,nil)) != sk2
| cons(A,nil) != sk3
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_63,c_15536]) ).
cnf(c_15537,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_66,c_54]) ).
cnf(c_328,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_63,c_15537]) ).
cnf(c_15538,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(paramod,[status(thm)],[c_66,c_53]) ).
cnf(c_329,plain,
ssList(sk6),
inference(resolve,[status(thm)],[c_63,c_15538]) ).
cnf(c_15539,plain,
( ~ neq(sk2,nil)
| cons(sk5,nil) = sk3 ),
inference(paramod,[status(thm)],[c_66,c_52]) ).
cnf(c_330,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_63,c_15539]) ).
cnf(c_15540,plain,
( ~ neq(sk4,nil)
| app(sk6,sk3) = sk4 ),
inference(paramod,[status(thm)],[c_330,c_51]) ).
cnf(c_15541,plain,
( ~ neq(sk4,nil)
| app(sk6,sk3) = sk2 ),
inference(paramod,[status(thm)],[c_66,c_15540]) ).
cnf(c_15542,plain,
( ~ neq(sk2,nil)
| app(sk6,sk3) = sk2 ),
inference(paramod,[status(thm)],[c_66,c_15541]) ).
cnf(c_331,plain,
app(sk6,sk3) = sk2,
inference(resolve,[status(thm)],[c_63,c_15542]) ).
cnf(c_15543,plain,
( app(A,cons(sk5,nil)) != sk2
| cons(sk5,nil) != sk3
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_328,c_327]) ).
cnf(c_15544,plain,
( app(A,cons(sk5,nil)) != sk2
| sk3 != sk3
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_330,c_15543]) ).
cnf(c_15545,plain,
( app(A,sk3) != sk2
| sk3 != sk3
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_330,c_15544]) ).
cnf(c_7935,plain,
( app(A,sk3) != sk2
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_15545]) ).
cnf(c_15546,plain,
app(sk6,sk3) != sk2,
inference(resolve,[status(thm)],[c_7935,c_329]) ).
cnf(c_15547,plain,
sk2 != sk2,
inference(paramod,[status(thm)],[c_331,c_15546]) ).
cnf(c_15534,plain,
$false,
inference(copy,[status(thm)],[c_15547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC096-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n001.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 12:20:43 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.40 % Process 1768882 was started by sandbox on n001,
% 0.13/0.40 % Sat Sep 26 12:20:43 2026
% 0.13/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.40
% 0.13/0.40 % From the command line: assign(max_seconds, 300).
% 23.06/3.38
% 23.06/3.38 % given #500 (I,wt=37): 569 app(app(A,cons(B,C)),cons(B,D)) != A | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf59(A),skaf60(A)). [factor(303,e,f),merge(g)].
% 23.06/3.38
% 23.06/3.38 % given #1000 (F,wt=9): 9776 -neq(skaf82(A),skaf82(A)). [resolve(396,b,218,a)].
% 23.06/3.38
% 23.06/3.38 % SZS status Unsatisfiable for theBenchmark
% 23.06/3.38
% 23.06/3.38 % Proof 1 at 2.25 (+ 0.68) seconds.
% 23.06/3.38 % Length of proof is 17.
% 23.06/3.38 % Level of proof is 4.
% 23.06/3.38 % Maximum clause weight is 25.000.
% 23.06/3.38 % Given clauses 1352.
% 23.06/3.38
% 23.06/3.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------