%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC258-1 : 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 : n003.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 08:57:18 AM UTC 2026
% Result : Unsatisfiable 11.38s 1.82s
% Output : CNFRefutation 11.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 33 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 7 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause4,axiom,
totalorderedP(nil),
file('theBenchmark.p',clause4) ).
cnf(c_48,plain,
totalorderedP(nil),
inference(clausify,[status(thm)],[clause4]) ).
fof(clause67,axiom,
! [VAR_0] :
( totalorderedP(cons(VAR_0,nil))
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',clause67) ).
cnf(c_106,plain,
( totalorderedP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[clause67]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_203,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_7,axiom,
~ totalorderedP(sk1),
file('theBenchmark.p',co1_7) ).
cnf(c_204,plain,
~ totalorderedP(sk1),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_205,plain,
~ totalorderedP(sk3),
inference(paramod,[status(thm)],[c_203,c_204]) ).
fof(co1_9,axiom,
( nil = sk3
| ssItem(sk5) ),
file('theBenchmark.p',co1_9) ).
cnf(c_208,plain,
( nil = sk3
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_209,plain,
( sk3 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_208]) ).
fof(co1_13,axiom,
( nil = sk3
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_13) ).
cnf(c_216,plain,
( nil = sk3
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_217,plain,
( sk3 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_216]) ).
cnf(c_7485,plain,
( totalorderedP(cons(sk5,nil))
| sk3 = nil ),
inference(resolve,[status(thm)],[c_209,c_106]) ).
cnf(c_7654,plain,
( ~ totalorderedP(nil)
| cons(sk5,nil) = sk3 ),
inference(paramod,[status(thm)],[c_217,c_205]) ).
cnf(c_7624,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_48,c_7654]) ).
cnf(c_7655,plain,
( totalorderedP(sk3)
| sk3 = nil ),
inference(paramod,[status(thm)],[c_7624,c_7485]) ).
cnf(c_7633,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_205,c_7655]) ).
cnf(c_7656,plain,
~ totalorderedP(nil),
inference(paramod,[status(thm)],[c_7633,c_205]) ).
cnf(c_7653,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_7656]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC258-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 12:39:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 2888198 was started by sandbox2 on n003,
% 0.12/0.36 % Sat Sep 26 12:39:39 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 11.38/1.82
% 11.38/1.82 % SZS status Unsatisfiable for theBenchmark
% 11.38/1.82
% 11.38/1.82 % Proof 1 at 1.17 (+ 0.25) seconds.
% 11.38/1.82 % Length of proof is 13.
% 11.38/1.82 % Level of proof is 4.
% 11.38/1.82 % Maximum clause weight is 12.000.
% 11.38/1.82 % Given clauses 168.
% 11.38/1.82
% 11.38/1.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------