%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC179-1 : 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 : n006.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 08:57:05 AM UTC 2026
% Result : Unsatisfiable 12.03s 6.95s
% Output : CNFRefutation 12.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 34 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 9 ( 4 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_18,axiom,
( nil = sk3
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_18) ).
cnf(c_48,plain,
( nil = sk3
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_18]) ).
cnf(c_49,plain,
( sk3 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_48]) ).
fof(co1_7,axiom,
~ duplicatefreeP(sk1),
file('theBenchmark.p',co1_7) ).
cnf(c_70,plain,
~ duplicatefreeP(sk1),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_71,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_74,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(clause72,axiom,
! [VAR_0,VAR_1] :
( ssItem(VAR_1)
| duplicatefreeP(VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause72) ).
cnf(c_169,plain,
( ssItem(B)
| duplicatefreeP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause72]) ).
fof(clause65,axiom,
! [VAR_0] :
( duplicatefreeP(cons(VAR_0,nil))
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',clause65) ).
cnf(c_173,plain,
( duplicatefreeP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[clause65]) ).
fof(clause2,axiom,
duplicatefreeP(nil),
file('theBenchmark.p',clause2) ).
cnf(c_232,plain,
duplicatefreeP(nil),
inference(clausify,[status(thm)],[clause2]) ).
cnf(c_298,plain,
~ duplicatefreeP(sk3),
inference(paramod,[status(thm)],[c_71,c_70]) ).
cnf(c_5773,plain,
( ssItem(A)
| duplicatefreeP(sk3) ),
inference(resolve,[status(thm)],[c_169,c_74]) ).
cnf(c_1602,plain,
ssItem(A),
inference(resolve,[status(thm)],[c_298,c_5773]) ).
cnf(c_2496,plain,
duplicatefreeP(cons(A,nil)),
inference(resolve,[status(thm)],[c_1602,c_173]) ).
cnf(c_5774,plain,
( duplicatefreeP(sk3)
| sk3 = nil ),
inference(paramod,[status(thm)],[c_49,c_2496]) ).
cnf(c_5769,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_298,c_5774]) ).
cnf(c_5775,plain,
~ duplicatefreeP(nil),
inference(paramod,[status(thm)],[c_5769,c_298]) ).
cnf(c_5772,plain,
$false,
inference(resolve,[status(thm)],[c_232,c_5775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC179-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n006.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 12:26:32 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 1257187 was started by sandbox2 on n006,
% 0.11/5.39 % Sat Sep 26 12:26:32 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.40
% 0.15/5.40 % From the command line: assign(max_seconds, 300).
% 12.03/6.95
% 12.03/6.95 % SZS status Unsatisfiable for theBenchmark
% 12.03/6.95
% 12.03/6.95 % Proof 1 at 1.33 (+ 0.20) seconds.
% 12.03/6.95 % Length of proof is 13.
% 12.03/6.95 % Level of proof is 5.
% 12.03/6.95 % Maximum clause weight is 8.000.
% 12.03/6.95 % Given clauses 252.
% 12.03/6.95
% 12.03/6.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------