%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA045-2 : 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 : n020.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 06:51:13 AM UTC 2026
% Result : Unsatisfiable 0.03s 0.37s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 22 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 15 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Ring__and__Field_Omult__cancel__right1_2,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = c_times(c_1,VAR_1,VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
cnf(c_1,plain,
( B = c_times(c_1,B,A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Omult__cancel__right1_2]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_2,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
! [VAR_0] :
( class_OrderedGroup_Olordered__ab__group__abs(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(c_3,plain,
( class_OrderedGroup_Olordered__ab__group__abs(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
fof(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(c_0,c_HOL_Oabs(VAR_1,VAR_0),VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(c_4,plain,
( c_lessequals(c_0,c_HOL_Oabs(B,A),A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c_5,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_6,plain,
c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b),
inference(resolve,[status(thm)],[c_4,c_5]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : ~ c_lessequals(c_0,c_times(VAR_0,c_HOL_Oabs(v_g(v_x(VAR_0)),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_7,plain,
~ c_lessequals(c_0,c_times(A,c_HOL_Oabs(v_g(v_x(A)),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_8,plain,
A = c_times(c_1,A,t_b),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_9,plain,
c_times(c_1,A,t_b) = A,
inference(copy,[status(thm)],[c_8]) ).
cnf(c_10,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_11,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA045-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.03/0.35 % CPULimit : 300
% 0.03/0.35 % WCLimit : 300
% 0.03/0.35 % DateTime : Sat Sep 26 22:11:04 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.36 % Process 2619358 was started by sandbox on n020,
% 0.03/0.36 % Sat Sep 26 22:11:04 2026
% 0.03/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.36
% 0.03/0.36 % From the command line: assign(max_seconds, 300).
% 0.03/0.37
% 0.03/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.03/0.37
% 0.03/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.37 % Length of proof is 11.
% 0.03/0.37 % Level of proof is 4.
% 0.03/0.37 % Maximum clause weight is 11.000.
% 0.03/0.37 % Given clauses 3.
% 0.03/0.37
% 0.03/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------