%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC422-1 : 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 : n026.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 08:57:46 AM UTC 2026
% Result : Unsatisfiable 78.67s 11.32s
% Output : CNFRefutation 78.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 13 unt; 0 def)
% Number of atoms : 91 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 110 ( 59 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_20,axiom,
( ~ neq(sk4,nil)
| app(app(sk7,cons(sk5,nil)),sk6) = sk3 ),
file('theBenchmark.p',co1_20) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| app(app(sk7,cons(sk5,nil)),sk6) = sk3 ),
inference(clausify,[status(thm)],[co1_20]) ).
fof(co1_19,axiom,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
file('theBenchmark.p',co1_19) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk4 ),
inference(clausify,[status(thm)],[co1_19]) ).
fof(co1_18,axiom,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('theBenchmark.p',co1_18) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| ssList(sk7) ),
inference(clausify,[status(thm)],[co1_18]) ).
fof(co1_17,axiom,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('theBenchmark.p',co1_17) ).
cnf(c_54,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_17]) ).
fof(co1_16,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_16) ).
cnf(c_55,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_16]) ).
fof(co1_15,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ neq(sk4,nil)
| app(app(VAR_2,cons(VAR_0,nil)),VAR_1) != sk1
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk2
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_15) ).
cnf(c_56,plain,
( ~ neq(sk4,nil)
| app(app(C,cons(A,nil)),B) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_15]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_64,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_65,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_64]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_66,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_67,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_68,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_67]) ).
cnf(c_8369,plain,
( ~ neq(sk4,nil)
| app(app(C,cons(A,nil)),B) != sk3
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_66,c_56]) ).
cnf(c_8370,plain,
( ~ neq(sk2,nil)
| app(app(C,cons(A,nil)),B) != sk3
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_68,c_8369]) ).
cnf(c_330,plain,
( app(app(C,cons(A,nil)),B) != sk3
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_65,c_8370]) ).
cnf(c_8371,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_68,c_55]) ).
cnf(c_331,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_65,c_8371]) ).
cnf(c_8372,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(paramod,[status(thm)],[c_68,c_54]) ).
cnf(c_332,plain,
ssList(sk6),
inference(resolve,[status(thm)],[c_65,c_8372]) ).
cnf(c_8373,plain,
( ~ neq(sk2,nil)
| ssList(sk7) ),
inference(paramod,[status(thm)],[c_68,c_53]) ).
cnf(c_333,plain,
ssList(sk7),
inference(resolve,[status(thm)],[c_65,c_8373]) ).
cnf(c_8374,plain,
( ~ neq(sk4,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk2 ),
inference(paramod,[status(thm)],[c_68,c_52]) ).
cnf(c_8375,plain,
( ~ neq(sk2,nil)
| app(app(sk6,cons(sk5,nil)),sk7) = sk2 ),
inference(paramod,[status(thm)],[c_68,c_8374]) ).
cnf(c_334,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk2,
inference(resolve,[status(thm)],[c_65,c_8375]) ).
cnf(c_8376,plain,
( ~ neq(sk2,nil)
| app(app(sk7,cons(sk5,nil)),sk6) = sk3 ),
inference(paramod,[status(thm)],[c_68,c_51]) ).
cnf(c_335,plain,
app(app(sk7,cons(sk5,nil)),sk6) = sk3,
inference(resolve,[status(thm)],[c_65,c_8376]) ).
cnf(c_8377,plain,
( app(app(sk7,cons(sk5,nil)),sk6) != sk3
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_334,c_330]) ).
cnf(c_8378,plain,
( sk3 != sk3
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(paramod,[status(thm)],[c_335,c_8377]) ).
cnf(c_8379,plain,
( ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssItem(sk5) ),
inference(copy,[status(thm)],[c_8378]) ).
cnf(c_8380,plain,
( ~ ssList(sk7)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_331,c_8379]) ).
cnf(c_8381,plain,
~ ssList(sk7),
inference(resolve,[status(thm)],[c_332,c_8380]) ).
cnf(c_8368,plain,
$false,
inference(resolve,[status(thm)],[c_333,c_8381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC422-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n026.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 13:04:25 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.36 % Process 1047414 was started by sandbox2 on n026,
% 0.07/0.36 % Sat Sep 26 13:04:25 2026
% 0.07/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.37
% 0.07/0.37 % From the command line: assign(max_seconds, 300).
% 78.67/11.32
% 78.67/11.32 % SZS status Unsatisfiable for theBenchmark
% 78.67/11.32
% 78.67/11.32 % Proof 1 at 2.20 (+ 0.62) seconds.
% 78.67/11.32 % Length of proof is 18.
% 78.67/11.32 % Level of proof is 3.
% 78.67/11.32 % Maximum clause weight is 39.000.
% 78.67/11.32 % Given clauses 270.
% 78.67/11.32
% 78.67/11.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------