%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA014-2 : 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 : n019.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 47 ( 18 unt; 0 def)
% Number of atoms : 78 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 31 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_2,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(clausify,[status(thm)],[tfree_tcs]) ).
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_3,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(clsrel_Ring__and__Field_Oordered__field_58,axiom,
! [VAR_0] :
( class_Orderings_Oorder(VAR_0)
| ~ class_Ring__and__Field_Oordered__field(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
cnf(c_4,plain,
( class_Orderings_Oorder(A)
| ~ class_Ring__and__Field_Oordered__field(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__field_58]) ).
fof(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,axiom,
! [VAR_0,VAR_1] :
( c_times(c_1,VAR_1,VAR_0) = VAR_1
| ~ class_OrderedGroup_Omonoid__mult(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
cnf(c_5,plain,
( c_times(c_1,B,A) = B
| ~ class_OrderedGroup_Omonoid__mult(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0]) ).
fof(clsrel_Ring__and__Field_Ofield_12,axiom,
! [VAR_0] :
( class_OrderedGroup_Omonoid__mult(VAR_0)
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
cnf(c_6,plain,
( class_OrderedGroup_Omonoid__mult(A)
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Ofield_12]) ).
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_7,plain,
( class_OrderedGroup_Osemigroup__mult(A)
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Ofield_21]) ).
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_8,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(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_9,plain,
( c_lessequals(B,B,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__class_Oaxioms__1_0]) ).
cnf(c_10,plain,
class_Orderings_Oorder(t_a),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_11,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(resolve,[status(thm)],[c_3,c_2]) ).
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_12,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]) ).
cnf(c_13,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolve,[status(thm)],[c_1,c_2]) ).
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_Ofield(A) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
fof(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0,axiom,
! [VAR_0,VAR_1] :
( c_times(c_HOL_Oinverse(VAR_1,VAR_0),VAR_1,VAR_0) = c_1
| VAR_1 = c_0
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
cnf(c_15,plain,
( c_times(c_HOL_Oinverse(B,A),B,A) = c_1
| B = c_0
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Ofield__class_Oaxioms__1_0]) ).
cnf(c_16,plain,
( ~ class_Ring__and__Field_Ofield(B)
| c_times(c_1,A,B) = A ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_17,plain,
c_times(c_1,A,t_a) = A,
inference(resolve,[status(thm)],[c_16,c_13]) ).
cnf(c_18,plain,
( c_times(c_HOL_Oinverse(A,t_a),A,t_a) = c_1
| A = c_0 ),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_19,plain,
( c_times(c_HOL_Oinverse(A,t_a),A,t_a) = c_1
| c_0 = A ),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_20,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_13,c_14]) ).
cnf(c_21,plain,
c_lessequals(A,A,t_a),
inference(resolve,[status(thm)],[c_9,c_10]) ).
fof(cls_conjecture_0,axiom,
v_c != c_0,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_22,plain,
v_c != c_0,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(VAR_0)),t_a),c_times(VAR_0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(VAR_0)),t_a),t_a),t_a),t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_23,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(A)),t_a),c_times(A,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(A)),t_a),t_a),t_a),t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_24,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_12]) ).
cnf(c_25,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_24]) ).
cnf(c_26,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(A)),t_a),c_times(A,c_HOL_Oabs(c_times(v_c,v_f(v_x(A)),t_a),t_a),t_a),t_a),
inference(paramod,[status(thm)],[c_25,c_23]) ).
cnf(c_45,plain,
( c_times(c_1,B,t_a) = c_times(c_HOL_Oinverse(A,t_a),c_times(A,B,t_a),t_a)
| c_0 = A ),
inference(paramod,[status(thm)],[c_19,c_20]) ).
cnf(c_46,plain,
( B = c_times(c_HOL_Oinverse(A,t_a),c_times(A,B,t_a),t_a)
| c_0 = A ),
inference(paramod,[status(thm)],[c_17,c_45]) ).
cnf(c_27,plain,
( c_times(c_HOL_Oinverse(A,t_a),c_times(A,B,t_a),t_a) = B
| c_0 = A ),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_34,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(A,t_a))),t_a),c_HOL_Oabs(c_times(A,c_times(v_c,v_f(v_x(c_HOL_Oabs(A,t_a))),t_a),t_a),t_a),t_a),
inference(paramod,[status(thm)],[c_25,c_26]) ).
cnf(c_47,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| c_0 = v_c ),
inference(paramod,[status(thm)],[c_27,c_34]) ).
cnf(c_48,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| v_c = c_0 ),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_49,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),
inference(resolve,[status(thm)],[c_22,c_48]) ).
cnf(c_44,plain,
$false,
inference(resolve,[status(thm)],[c_21,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA014-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 22:04:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2283484 was started by sandbox on n019,
% 0.08/0.36 % Sat Sep 26 22:04:48 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 29.
% 0.13/0.38 % Level of proof is 6.
% 0.13/0.38 % Maximum clause weight is 22.000.
% 0.13/0.38 % Given clauses 10.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------