%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV254-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 09:07:09 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 16 unt; 0 def)
% Number of atoms : 24 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 27 ( 9 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_nat_3,axiom,
class_Orderings_Oorder(tc_nat),
file('theBenchmark.p',clsarity_nat_3) ).
cnf(c_1,plain,
class_Orderings_Oorder(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat_3]) ).
fof(cls_SetInterval_OatLeastLessThan__empty_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_SetInterval_OatLeastLessThan(VAR_2,VAR_1,VAR_0) = c_emptyset
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
cnf(c_2,plain,
( c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset
| ~ c_lessequals(B,C,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_SetInterval_OatLeastLessThan__empty_0]) ).
cnf(c_3,plain,
( c_SetInterval_OatLeastLessThan(B,A,tc_nat) = c_emptyset
| ~ c_lessequals(A,B,tc_nat) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : v_x(VAR_0) = v_nat,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_4,plain,
v_x(A) = v_nat,
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : c_lessequals(VAR_0,v_x(VAR_0),tc_nat),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_5,plain,
c_lessequals(A,v_x(A),tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_6,plain,
c_lessequals(A,v_nat,tc_nat),
inference(paramod,[status(thm)],[c_4,c_5]) ).
fof(cls_Set_Oempty__not__insert_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_emptyset != c_insert(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
cnf(c_7,plain,
c_emptyset != c_insert(A,B,C),
inference(clausify,[status(thm)],[cls_Set_Oempty__not__insert_0]) ).
cnf(c_8,plain,
c_insert(A,B,C) != c_emptyset,
inference(copy,[status(thm)],[c_7]) ).
fof(cls_SetInterval_OatLeastLessThan__singleton_0,axiom,
! [VAR_0] : c_SetInterval_OatLeastLessThan(VAR_0,c_Suc(VAR_0),tc_nat) = c_insert(VAR_0,c_emptyset,tc_nat),
file('theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
cnf(c_9,plain,
c_SetInterval_OatLeastLessThan(A,c_Suc(A),tc_nat) = c_insert(A,c_emptyset,tc_nat),
inference(clausify,[status(thm)],[cls_SetInterval_OatLeastLessThan__singleton_0]) ).
cnf(c_10,plain,
c_insert(A,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(A,c_Suc(A),tc_nat),
inference(copy,[status(thm)],[c_9]) ).
cnf(c_11,plain,
c_SetInterval_OatLeastLessThan(v_nat,A,tc_nat) = c_emptyset,
inference(resolve,[status(thm)],[c_3,c_6]) ).
cnf(c_12,plain,
c_SetInterval_OatLeastLessThan(A,c_Suc(A),tc_nat) != c_emptyset,
inference(paramod,[status(thm)],[c_10,c_8]) ).
cnf(c_13,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV254-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.38 % Computer : n004.cluster.edu
% 0.07/0.38 % Model : x86_64 x86_64
% 0.07/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.38 % Memory : 8046.5625MB
% 0.07/0.38 % OS : Linux 6.8.0-71-generic
% 0.07/0.38 % CPULimit : 300
% 0.07/0.38 % WCLimit : 300
% 0.07/0.38 % DateTime : Sat Sep 26 13:23:21 UTC 2026
% 0.07/0.39 % CPUTime :
% 0.07/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.39 % Process 1815244 was started by sandbox on n004,
% 0.07/0.39 % Sat Sep 26 13:23:21 2026
% 0.07/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.39
% 0.07/0.39 % From the command line: assign(max_seconds, 300).
% 0.11/0.40
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.40 % Length of proof is 13.
% 0.11/0.40 % Level of proof is 3.
% 0.11/0.40 % Maximum clause weight is 10.000.
% 0.11/0.40 % Given clauses 5.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------