%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA015-2 : 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 : 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 06:51:07 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 71 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 67 ( 35 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 76 ( 3 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_Ring__and__Field_Oordered__field_47,axiom,
! [VAR_0] :
( class_OrderedGroup_Olordered__ab__group__abs(VAR_0)
| ~ class_Ring__and__Field_Oordered__field(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
cnf(c_1,plain,
( class_OrderedGroup_Olordered__ab__group__abs(A)
| ~ class_Ring__and__Field_Oordered__field(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_47]) ).
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_2,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]) ).
fof(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_times(c_times(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_times(VAR_1,c_times(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_OrderedGroup_Osemigroup__mult(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
cnf(c_3,plain,
( c_times(c_times(B,C,A),D,A) = c_times(B,c_times(C,D,A),A)
| ~ class_OrderedGroup_Osemigroup__mult(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0]) ).
fof(clsrel_Ring__and__Field_Ofield_21,axiom,
! [VAR_0] :
( class_OrderedGroup_Osemigroup__mult(VAR_0)
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
cnf(c_4,plain,
( class_OrderedGroup_Osemigroup__mult(A)
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Ofield_21]) ).
fof(clsrel_Ring__and__Field_Oordered__field_34,axiom,
! [VAR_0] :
( class_Ring__and__Field_Oordered__idom(VAR_0)
| ~ class_Ring__and__Field_Oordered__field(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
cnf(c_5,plain,
( class_Ring__and__Field_Oordered__idom(A)
| ~ class_Ring__and__Field_Oordered__field(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_34]) ).
fof(cls_Ring__and__Field_Oabs__mult_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_HOL_Oabs(c_times(VAR_1,VAR_2,VAR_0),VAR_0) = c_times(c_HOL_Oabs(VAR_1,VAR_0),c_HOL_Oabs(VAR_2,VAR_0),VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(c_6,plain,
( c_HOL_Oabs(c_times(B,C,A),A) = c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Oabs__mult_0]) ).
fof(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_times(VAR_3,VAR_1,VAR_0),c_times(VAR_3,VAR_2,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__left__mono_0) ).
cnf(c_7,plain,
( c_lessequals(c_times(D,B,A),c_times(D,C,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__left__mono_0]) ).
fof(clsrel_Ring__and__Field_Oordered__field_46,axiom,
! [VAR_0] :
( class_Ring__and__Field_Opordered__semiring(VAR_0)
| ~ class_Ring__and__Field_Oordered__field(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).
cnf(c_8,plain,
( class_Ring__and__Field_Opordered__semiring(A)
| ~ class_Ring__and__Field_Oordered__field(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_46]) ).
fof(clsrel_Ring__and__Field_Oordered__field_0,axiom,
! [VAR_0] :
( class_Ring__and__Field_Ofield(VAR_0)
| ~ class_Ring__and__Field_Oordered__field(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
cnf(c_9,plain,
( class_Ring__and__Field_Ofield(A)
| ~ class_Ring__and__Field_Oordered__field(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_0]) ).
cnf(c_10,plain,
( ~ class_Ring__and__Field_Ofield(C)
| c_times(c_times(A,B,C),D,C) = c_times(A,c_times(B,D,C),C) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_11,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(clausify,[status(thm)],[tfree_tcs]) ).
cnf(c_12,plain,
( c_lessequals(c_0,c_HOL_Oabs(B,A),A)
| ~ class_Ring__and__Field_Oordered__field(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_13,plain,
( c_HOL_Oabs(c_times(B,C,A),A) = c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A)
| ~ class_Ring__and__Field_Oordered__field(A) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_14,plain,
( c_times(c_times(B,C,A),D,A) = c_times(B,c_times(C,D,A),A)
| ~ class_Ring__and__Field_Oordered__field(A) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_15,plain,
( ~ class_Ring__and__Field_Oordered__field(C)
| c_lessequals(c_times(D,A,C),c_times(D,B,C),C)
| ~ c_lessequals(c_0,D,C)
| ~ c_lessequals(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_16,plain,
( c_lessequals(c_times(C,A,t_a),c_times(C,B,t_a),t_a)
| ~ c_lessequals(c_0,C,t_a)
| ~ c_lessequals(A,B,t_a) ),
inference(resolve,[status(thm)],[c_15,c_11]) ).
cnf(c_17,plain,
c_times(c_times(A,B,t_a),C,t_a) = c_times(A,c_times(B,C,t_a),t_a),
inference(resolve,[status(thm)],[c_11,c_14]) ).
cnf(c_18,plain,
c_HOL_Oabs(c_times(A,B,t_a),t_a) = c_times(c_HOL_Oabs(A,t_a),c_HOL_Oabs(B,t_a),t_a),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_19,plain,
c_times(c_HOL_Oabs(A,t_a),c_HOL_Oabs(B,t_a),t_a) = c_HOL_Oabs(c_times(A,B,t_a),t_a),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_20,plain,
c_lessequals(c_0,c_HOL_Oabs(A,t_a),t_a),
inference(resolve,[status(thm)],[c_11,c_12]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_lessequals(c_HOL_Oabs(v_g(VAR_0),t_a),c_times(v_d,c_HOL_Oabs(v_f(VAR_0),t_a),t_a),t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_21,plain,
c_lessequals(c_HOL_Oabs(v_g(A),t_a),c_times(v_d,c_HOL_Oabs(v_f(A),t_a),t_a),t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(VAR_0)),t_a),t_a),c_times(VAR_0,c_HOL_Oabs(v_f(v_x(VAR_0)),t_a),t_a),t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_22,plain,
~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(A)),t_a),t_a),c_times(A,c_HOL_Oabs(v_f(v_x(A)),t_a),t_a),t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_28,plain,
( c_lessequals(c_times(A,c_HOL_Oabs(v_g(B),t_a),t_a),c_times(A,c_times(v_d,c_HOL_Oabs(v_f(B),t_a),t_a),t_a),t_a)
| ~ c_lessequals(c_0,A,t_a) ),
inference(resolve,[status(thm)],[c_16,c_21]) ).
cnf(c_29,plain,
c_lessequals(c_times(c_HOL_Oabs(A,t_a),c_HOL_Oabs(v_g(B),t_a),t_a),c_times(c_HOL_Oabs(A,t_a),c_times(v_d,c_HOL_Oabs(v_f(B),t_a),t_a),t_a),t_a),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_25,plain,
c_lessequals(c_HOL_Oabs(c_times(A,v_g(B),t_a),t_a),c_times(c_HOL_Oabs(A,t_a),c_times(v_d,c_HOL_Oabs(v_f(B),t_a),t_a),t_a),t_a),
inference(paramod,[status(thm)],[c_19,c_29]) ).
cnf(c_26,plain,
~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(A,B,t_a))),t_a),t_a),c_times(A,c_times(B,c_HOL_Oabs(v_f(v_x(c_times(A,B,t_a))),t_a),t_a),t_a),t_a),
inference(paramod,[status(thm)],[c_17,c_22]) ).
cnf(c_27,plain,
$false,
inference(resolve,[status(thm)],[c_26,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA015-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 22:06:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3871564 was started by sandbox on n003,
% 0.11/0.37 % Sat Sep 26 22:06:09 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 25.
% 0.11/0.38 % Level of proof is 5.
% 0.11/0.38 % Maximum clause weight is 29.000.
% 0.11/0.38 % Given clauses 6.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------