%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA020-2 : 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 : n005.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 06:51:08 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 22 unt; 0 def)
% Number of atoms : 63 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 31 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 3 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Orderings_Oorder__less__imp__le_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ c_less(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(c_1,plain,
( c_lessequals(B,C,A)
| ~ c_less(B,C,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__less__imp__le_0]) ).
fof(cls_conjecture_1,axiom,
c_less(c_0,v_c,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
c_less(c_0,v_c,t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_3,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(clausify,[status(thm)],[tfree_tcs]) ).
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_4,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(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_5,plain,
( class_Orderings_Oorder(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]) ).
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_6,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__eq__0_1,axiom,
! [VAR_0] :
( c_HOL_Oabs(c_0,VAR_0) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
cnf(c_7,plain,
( c_HOL_Oabs(c_0,A) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oabs__eq__0_1]) ).
cnf(c_8,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolve,[status(thm)],[c_3,c_6]) ).
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_9,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_10,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(resolve,[status(thm)],[c_3,c_4]) ).
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_11,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_12,plain,
( c_lessequals(c_0,c_times(B,A,t_a),t_a)
| ~ c_lessequals(c_0,B,t_a)
| ~ c_lessequals(c_0,A,t_a) ),
inference(resolve,[status(thm)],[c_10,c_11]) ).
cnf(c_13,plain,
class_Orderings_Oorder(t_a),
inference(resolve,[status(thm)],[c_3,c_5]) ).
fof(cls_conjecture_0,axiom,
v_f(c_0) = c_0,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_14,plain,
v_f(c_0) = c_0,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_3,axiom,
v_x = c_0,
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_15,plain,
v_x = c_0,
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_16,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_27,plain,
~ c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_28,plain,
~ c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(paramod,[status(thm)],[c_14,c_27]) ).
cnf(c_17,plain,
~ c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_c,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(paramod,[status(thm)],[c_15,c_28]) ).
cnf(c_18,plain,
( c_lessequals(c_0,v_c,t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_19,plain,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_20,plain,
c_lessequals(c_0,c_HOL_Oabs(A,t_a),t_a),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_21,plain,
~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(paramod,[status(thm)],[c_19,c_17]) ).
cnf(c_22,plain,
c_lessequals(c_0,v_c,t_a),
inference(resolve,[status(thm)],[c_18,c_13]) ).
cnf(c_29,plain,
( c_lessequals(c_0,c_times(A,c_HOL_Oabs(B,t_a),t_a),t_a)
| ~ c_lessequals(c_0,A,t_a) ),
inference(resolve,[status(thm)],[c_12,c_20]) ).
cnf(c_25,plain,
~ c_lessequals(c_0,v_c,t_a),
inference(resolve,[status(thm)],[c_29,c_21]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA020-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n005.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 22:05:32 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 3204441 was started by sandbox on n005,
% 0.19/0.46 % Sat Sep 26 22:05:32 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.48 % Length of proof is 24.
% 0.19/0.48 % Level of proof is 5.
% 0.19/0.48 % Maximum clause weight is 15.000.
% 0.19/0.48 % Given clauses 8.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------