%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA009-2 : 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 : 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 06:51:06 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.59s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 35 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 31 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_Ring__and__Field_Oordered__idom_37,axiom,
! [VAR_0] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
cnf(c_1,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_37]) ).
fof(cls_OrderedGroup_Oadd__le__cancel__right_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_plus(VAR_1,VAR_3,VAR_0),c_plus(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
cnf(c_2,plain,
( c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A)
| ~ c_lessequals(B,C,A)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oadd__le__cancel__right_1]) ).
fof(cls_OrderedGroup_Oright__minus_0,axiom,
! [VAR_0,VAR_1] :
( c_plus(VAR_1,c_uminus(VAR_1,VAR_0),VAR_0) = c_0
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
cnf(c_3,plain,
( c_plus(B,c_uminus(B,A),A) = c_0
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oright__minus_0]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
! [VAR_0] :
( class_OrderedGroup_Oab__group__add(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(c_4,plain,
( class_OrderedGroup_Oab__group__add(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_4]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_5,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
cnf(c_6,plain,
( ~ class_Ring__and__Field_Oordered__idom(B)
| c_plus(A,c_uminus(A,B),B) = c_0 ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
cnf(c_7,plain,
( c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A)
| ~ c_lessequals(B,C,A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
( c_lessequals(c_plus(A,C,t_b),c_plus(B,C,t_b),t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_9,plain,
c_plus(A,c_uminus(A,t_b),t_b) = c_0,
inference(resolve,[status(thm)],[c_5,c_6]) ).
fof(cls_conjecture_2,axiom,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_10,plain,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : c_lessequals(v_lb(VAR_0),v_f(VAR_0),t_b),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_11,plain,
c_lessequals(v_lb(A),v_f(A),t_b),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_12,plain,
c_lessequals(c_plus(v_lb(A),B,t_b),c_plus(v_f(A),B,t_b),t_b),
inference(resolve,[status(thm)],[c_8,c_11]) ).
cnf(c_14,plain,
c_lessequals(c_0,c_plus(v_f(A),c_uminus(v_lb(A),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_9,c_12]) ).
cnf(c_15,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n006.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sat Sep 26 22:03:42 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.58 % Process 2220099 was started by sandbox on n006,
% 0.09/0.58 % Sat Sep 26 22:03:42 2026
% 0.09/0.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.58
% 0.09/0.58 % From the command line: assign(max_seconds, 300).
% 0.09/0.59
% 0.09/0.59 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.59
% 0.09/0.59 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.59 % Length of proof is 14.
% 0.09/0.59 % Level of proof is 5.
% 0.09/0.59 % Maximum clause weight is 14.000.
% 0.09/0.59 % Given clauses 5.
% 0.09/0.59
% 0.09/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------