%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA039-2 : 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 : 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 06:51:12 AM UTC 2026
% Result : Unsatisfiable 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 31 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 46 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
! [VAR_0] :
( class_Ring__and__Field_Opordered__semiring(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
cnf(c_1,plain,
( class_Ring__and__Field_Opordered__semiring(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_42]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_2,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(clausify,[status(thm)],[tfree_tcs]) ).
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_3,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_4,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_5,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_6,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolve,[status(thm)],[c_4,c_2]) ).
fof(cls_OrderedGroup_Oabs__ge__self_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_1,c_HOL_Oabs(VAR_1,VAR_0),VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__ge__self_0) ).
cnf(c_7,plain,
( c_lessequals(B,c_HOL_Oabs(B,A),A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oabs__ge__self_0]) ).
cnf(c_8,plain,
class_Orderings_Oorder(t_a),
inference(resolve,[status(thm)],[c_3,c_2]) ).
fof(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_3,VAR_2,VAR_0)
| ~ c_lessequals(VAR_3,VAR_1,VAR_0)
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(c_9,plain,
( c_lessequals(D,C,A)
| ~ c_lessequals(D,B,A)
| ~ c_lessequals(B,C,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
fof(cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_times(VAR_1,VAR_3,VAR_0),c_times(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ c_lessequals(c_0,VAR_3,VAR_0)
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Ring__and__Field_Opordered__semiring(VAR_0) ),
file('theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).
cnf(c_10,plain,
( c_lessequals(c_times(B,D,A),c_times(C,D,A),A)
| ~ c_lessequals(c_0,D,A)
| ~ c_lessequals(B,C,A)
| ~ class_Ring__and__Field_Opordered__semiring(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0]) ).
cnf(c_11,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_12,plain,
( c_lessequals(c_times(A,C,t_a),c_times(B,C,t_a),t_a)
| ~ c_lessequals(c_0,C,t_a)
| ~ c_lessequals(A,B,t_a) ),
inference(resolve,[status(thm)],[c_10,c_11]) ).
cnf(c_13,plain,
c_lessequals(A,c_HOL_Oabs(A,t_a),t_a),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_14,plain,
c_lessequals(c_0,c_HOL_Oabs(A,t_a),t_a),
inference(resolve,[status(thm)],[c_5,c_6]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : c_lessequals(c_HOL_Oabs(v_h(VAR_0),t_a),c_times(v_c,c_HOL_Oabs(v_f(VAR_0),t_a),t_a),t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_15,plain,
c_lessequals(c_HOL_Oabs(v_h(A),t_a),c_times(v_c,c_HOL_Oabs(v_f(A),t_a),t_a),t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_2,axiom,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_16,plain,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_17,plain,
( c_lessequals(C,B,t_a)
| ~ c_lessequals(C,A,t_a)
| ~ c_lessequals(A,B,t_a) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_29,plain,
( c_lessequals(c_times(B,A,t_a),c_times(c_HOL_Oabs(B,t_a),A,t_a),t_a)
| ~ c_lessequals(c_0,A,t_a) ),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_20,plain,
c_lessequals(c_times(A,c_HOL_Oabs(B,t_a),t_a),c_times(c_HOL_Oabs(A,t_a),c_HOL_Oabs(B,t_a),t_a),t_a),
inference(resolve,[status(thm)],[c_29,c_14]) ).
cnf(c_30,plain,
( c_lessequals(c_HOL_Oabs(v_h(A),t_a),B,t_a)
| ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(A),t_a),t_a),B,t_a) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_27,plain,
~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_a),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(resolve,[status(thm)],[c_30,c_16]) ).
cnf(c_28,plain,
$false,
inference(resolve,[status(thm)],[c_27,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n005.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 22:09:22 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 3214176 was started by sandbox2 on n005,
% 0.09/5.37 % Sat Sep 26 22:09:22 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.39 % Length of proof is 20.
% 0.09/5.39 % Level of proof is 4.
% 0.09/5.39 % Maximum clause weight is 18.000.
% 0.09/5.39 % Given clauses 6.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------