%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA013-1 : 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 : 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 06:51:06 AM UTC 2026
% Result : Unsatisfiable 41.20s 6.52s
% Output : CNFRefutation 41.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 9 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
! [VAR_0] :
( class_Orderings_Oorder(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
cnf(c_436,plain,
( class_Orderings_Oorder(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]) ).
fof(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_1,VAR_1,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
cnf(c_1050,plain,
( c_lessequals(B,B,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__class_Oaxioms__1_0]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : ~ c_lessequals(c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_f(v_x(VAR_0)),t_b),t_b),c_times(VAR_0,c_HOL_Oabs(v_f(v_x(VAR_0)),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_3321,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_f(v_x(A)),t_b),t_b),c_times(A,c_HOL_Oabs(v_f(v_x(A)),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_3322,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
cnf(c_12195,plain,
class_Orderings_Oorder(t_b),
inference(resolve,[status(thm)],[c_3322,c_436]) ).
cnf(c_12840,plain,
c_lessequals(A,A,t_b),
inference(resolve,[status(thm)],[c_12195,c_1050]) ).
cnf(c_12841,plain,
$false,
inference(resolve,[status(thm)],[c_12840,c_3321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA013-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.39 % Computer : n003.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sat Sep 26 22:05:55 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.39 % Process 3871173 was started by sandbox on n003,
% 0.10/0.39 % Sat Sep 26 22:05:55 2026
% 0.10/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 41.20/6.52
% 41.20/6.52 % given #500 (I,wt=9): 813 -class_OrderedGroup_Olordered__ab__group(A) | class_Orderings_Oord(A) # tptp_name(clsrel_OrderedGroup_Olordered__ab__group_9) # clausal_fof(1). [assumption].
% 41.20/6.52
% 41.20/6.52 % given #1000 (I,wt=20): 1376 -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | c_divide(c_1,c_0,A) = c_0. [copy(1375),flip(c)].
% 41.20/6.52
% 41.20/6.52 % given #1500 (I,wt=26): 1977 -class_HOL_Oone(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A) # tptp_name(cls_NatSimprocs_Ominus__less__iff__1_0) # clausal_fof(1). [assumption].
% 41.20/6.52
% 41.20/6.52 % given #2000 (I,wt=16): 2612 c_Divides_Oop_Amod(A,c_0,tc_IntDef_Oint) = A # tptp_name(cls_IntDiv_ODIVISION__BY__ZERO_0) # clausal_fof(1). [assumption].
% 41.20/6.52
% 41.20/6.52 % given #2500 (I,wt=9): 3237 -class_Ring__and__Field_Opordered__cancel__semiring(A) | class_HOL_Ozero(A) # tptp_name(clsrel_Ring__and__Field_Opordered__cancel__semiring_6) # clausal_fof(1). [assumption].
% 41.20/6.52
% 41.20/6.52 % SZS status Unsatisfiable for theBenchmark
% 41.20/6.52
% 41.20/6.52 % Proof 1 at 5.27 (+ 0.49) seconds.
% 41.20/6.52 % Length of proof is 7.
% 41.20/6.52 % Level of proof is 3.
% 41.20/6.52 % Maximum clause weight is 45.000.
% 41.20/6.52 % Given clauses 2823.
% 41.20/6.52
% 41.20/6.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------