%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA044-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 43 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 7 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
! [VAR_0] :
( class_Ring__and__Field_Opordered__cancel__semiring(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
cnf(c_1,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_40]) ).
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__of__nonneg_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oabs(VAR_1,VAR_0) = VAR_1
| ~ c_lessequals(c_0,VAR_1,VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
cnf(c_4,plain,
( c_HOL_Oabs(B,A) = B
| ~ c_lessequals(c_0,B,A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oabs__of__nonneg_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,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(c_0,c_times(VAR_2,VAR_1,VAR_0),VAR_0)
| ~ c_lessequals(c_0,VAR_2,VAR_0)
| ~ c_lessequals(c_0,VAR_1,VAR_0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(VAR_0) ),
file('theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
cnf(c_7,plain,
( c_lessequals(c_0,c_times(C,B,A),A)
| ~ c_lessequals(c_0,C,A)
| ~ c_lessequals(c_0,B,A)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Omult__nonneg__nonneg_0]) ).
cnf(c_8,plain,
( c_lessequals(c_0,c_times(B,A,t_b),t_b)
| ~ c_lessequals(c_0,B,t_b)
| ~ c_lessequals(c_0,A,t_b) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
fof(cls_conjecture_3,axiom,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_9,plain,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_10,plain,
c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) != c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),
inference(copy,[status(thm)],[c_9]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_lessequals(c_0,v_h(VAR_0),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_11,plain,
c_lessequals(c_0,v_h(A),t_b),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(c_0,v_l(VAR_0,VAR_1),t_b),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_12,plain,
c_lessequals(c_0,v_l(A,B),t_b),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_13,plain,
( c_HOL_Oabs(A,t_b) = A
| ~ c_lessequals(c_0,A,t_b) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_22,plain,
( c_lessequals(c_0,c_times(A,v_h(B),t_b),t_b)
| ~ c_lessequals(c_0,A,t_b) ),
inference(resolve,[status(thm)],[c_8,c_11]) ).
cnf(c_16,plain,
c_lessequals(c_0,c_times(v_l(A,B),v_h(C),t_b),t_b),
inference(resolve,[status(thm)],[c_22,c_12]) ).
cnf(c_20,plain,
~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_21,plain,
$false,
inference(resolve,[status(thm)],[c_20,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA044-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 22:13:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2045506 was started by sandbox2 on n026,
% 0.10/0.37 % Sat Sep 26 22:13:11 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 16.
% 0.14/0.38 % Level of proof is 4.
% 0.14/0.38 % Maximum clause weight is 21.000.
% 0.14/0.38 % Given clauses 5.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------