%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA026-2 : 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 06:51:09 AM UTC 2026
% Result : Unsatisfiable 1.47s 0.87s
% Output : CNFRefutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 30
% Syntax : Number of formulae : 130 ( 56 unt; 0 def)
% Number of atoms : 233 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 222 ( 119 ~; 103 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 238 ( 3 sgn 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
! [VAR_0] :
( class_OrderedGroup_Ocomm__monoid__add(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(c_1,plain,
( class_OrderedGroup_Ocomm__monoid__add(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_23]) ).
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_33,axiom,
! [VAR_0] :
( class_Orderings_Olinorder(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(c_3,plain,
( class_Orderings_Olinorder(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
! [VAR_0] :
( class_LOrder_Ojoin__semilorder(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
cnf(c_4,plain,
( class_LOrder_Ojoin__semilorder(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_35]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
! [VAR_0] :
( class_OrderedGroup_Oab__group__add(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(c_5,plain,
( class_OrderedGroup_Oab__group__add(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_4]) ).
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_Ominus__diff__eq_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_uminus(c_minus(VAR_1,VAR_2,VAR_0),VAR_0) = c_minus(VAR_2,VAR_1,VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
cnf(c_7,plain,
( c_uminus(c_minus(B,C,A),A) = c_minus(C,B,A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ominus__diff__eq_0]) ).
cnf(c_8,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolve,[status(thm)],[c_5,c_2]) ).
fof(cls_OrderedGroup_Odiff__self_0,axiom,
! [VAR_0,VAR_1] :
( c_minus(VAR_1,VAR_1,VAR_0) = c_0
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
cnf(c_9,plain,
( c_minus(B,B,A) = c_0
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Odiff__self_0]) ).
fof(cls_OrderedGroup_Ocompare__rls__4_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_minus(c_minus(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_minus(VAR_1,c_plus(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__4_0) ).
cnf(c_10,plain,
( c_minus(c_minus(B,C,A),D,A) = c_minus(B,c_plus(C,D,A),A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__4_0]) ).
fof(cls_OrderedGroup_Ocompare__rls__2_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_plus(VAR_1,c_minus(VAR_2,VAR_3,VAR_0),VAR_0) = c_minus(c_plus(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
cnf(c_12,plain,
( c_plus(B,c_minus(C,D,A),A) = c_minus(c_plus(B,C,A),D,A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__2_0]) ).
fof(cls_OrderedGroup_Ocompare__rls__10_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_minus(c_plus(VAR_1,VAR_2,VAR_0),VAR_2,VAR_0) = VAR_1
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__10_1) ).
cnf(c_13,plain,
( c_minus(c_plus(B,C,A),C,A) = B
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__10_1]) ).
fof(cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_minus(VAR_1,VAR_2,VAR_0) = c_plus(VAR_1,c_uminus(VAR_2,VAR_0),VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0) ).
cnf(c_14,plain,
( c_minus(B,C,A) = c_plus(B,c_uminus(C,A),A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0]) ).
cnf(c_15,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolve,[status(thm)],[c_6,c_2]) ).
fof(clsrel_OrderedGroup_Olordered__ab__group__abs_6,axiom,
! [VAR_0] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
cnf(c_16,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[clsrel_OrderedGroup_Olordered__ab__group__abs_6]) ).
fof(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
! [VAR_0] :
( class_OrderedGroup_Opordered__ab__group__add(VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
cnf(c_17,plain,
( class_OrderedGroup_Opordered__ab__group__add(A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[clsrel_OrderedGroup_Olordered__ab__group__abs_1]) ).
fof(cls_OrderedGroup_Oabs__of__nonpos_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oabs(VAR_1,VAR_0) = c_uminus(VAR_1,VAR_0)
| ~ c_lessequals(VAR_1,c_0,VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
cnf(c_18,plain,
( c_HOL_Oabs(B,A) = c_uminus(B,A)
| ~ c_lessequals(B,c_0,A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oabs__of__nonpos_0]) ).
fof(cls_OrderedGroup_Oabs__minus__cancel_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oabs(c_uminus(VAR_1,VAR_0),VAR_0) = c_HOL_Oabs(VAR_1,VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
cnf(c_19,plain,
( c_HOL_Oabs(c_uminus(B,A),A) = c_HOL_Oabs(B,A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oabs__minus__cancel_0]) ).
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_20,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_Oadd__le__cancel__right_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_1,VAR_3,VAR_0)
| ~ c_lessequals(c_plus(VAR_1,VAR_2,VAR_0),c_plus(VAR_3,VAR_2,VAR_0),VAR_0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
cnf(c_21,plain,
( c_lessequals(B,D,A)
| ~ c_lessequals(c_plus(B,C,A),c_plus(D,C,A),A)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oadd__le__cancel__right_0]) ).
cnf(c_22,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(resolve,[status(thm)],[c_15,c_16]) ).
fof(cls_OrderedGroup_Oadd__le__cancel__left_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_plus(VAR_3,VAR_1,VAR_0),c_plus(VAR_3,VAR_2,VAR_0),VAR_0)
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
cnf(c_23,plain,
( c_lessequals(c_plus(D,B,A),c_plus(D,C,A),A)
| ~ c_lessequals(B,C,A)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oadd__le__cancel__left_1]) ).
cnf(c_24,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
! [VAR_0,VAR_1] :
( c_plus(c_0,VAR_1,VAR_0) = VAR_1
| ~ class_OrderedGroup_Ocomm__monoid__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(c_25,plain,
( c_plus(c_0,B,A) = B
| ~ class_OrderedGroup_Ocomm__monoid__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0]) ).
fof(cls_OrderedGroup_Ocompare__rls__8_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_minus(VAR_1,VAR_3,VAR_0),VAR_2,VAR_0)
| ~ c_lessequals(VAR_1,c_plus(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
cnf(c_26,plain,
( c_lessequals(c_minus(B,D,A),C,A)
| ~ c_lessequals(B,c_plus(C,D,A),A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__8_1]) ).
cnf(c_27,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolve,[status(thm)],[c_15,c_17]) ).
fof(cls_OrderedGroup_Ocompare__rls__6_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_less(VAR_1,c_plus(VAR_3,VAR_2,VAR_0),VAR_0)
| ~ c_less(c_minus(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__6_0) ).
cnf(c_28,plain,
( c_less(B,c_plus(D,C,A),A)
| ~ c_less(c_minus(B,C,A),D,A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__6_0]) ).
cnf(c_29,plain,
class_Orderings_Olinorder(t_b),
inference(resolve,[status(thm)],[c_3,c_2]) ).
fof(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Orderings_Omax(VAR_3,VAR_1,VAR_0),VAR_2,VAR_0)
| ~ c_lessequals(VAR_3,VAR_2,VAR_0)
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
cnf(c_30,plain,
( c_lessequals(c_Orderings_Omax(D,B,A),C,A)
| ~ c_lessequals(D,C,A)
| ~ c_lessequals(B,C,A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2]) ).
fof(cls_Orderings_Olinorder__not__le_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_lessequals(VAR_2,VAR_1,VAR_0)
| ~ c_less(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Olinorder__not__le_1) ).
cnf(c_31,plain,
( ~ c_lessequals(C,B,A)
| ~ c_less(B,C,A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Olinorder__not__le_1]) ).
fof(cls_Orderings_Olinorder__not__le_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_2,VAR_1,VAR_0)
| c_less(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
cnf(c_32,plain,
( c_lessequals(C,B,A)
| c_less(B,C,A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Olinorder__not__le_0]) ).
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_33,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(clsrel_LOrder_Ojoin__semilorder_1,axiom,
! [VAR_0] :
( class_Orderings_Oorder(VAR_0)
| ~ class_LOrder_Ojoin__semilorder(VAR_0) ),
file('theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
cnf(c_34,plain,
( class_Orderings_Oorder(A)
| ~ class_LOrder_Ojoin__semilorder(A) ),
inference(clausify,[status(thm)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
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_35,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]) ).
cnf(c_36,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_37,plain,
( ~ class_LOrder_Ojoin__semilorder(C)
| c_lessequals(A,B,C)
| ~ c_less(A,B,C) ),
inference(resolve,[status(thm)],[c_33,c_34]) ).
cnf(c_38,plain,
( ~ class_LOrder_Ojoin__semilorder(C)
| c_lessequals(D,B,C)
| ~ c_lessequals(D,A,C)
| ~ c_lessequals(A,B,C) ),
inference(resolve,[status(thm)],[c_35,c_34]) ).
cnf(c_39,plain,
( c_lessequals(C,B,t_b)
| ~ c_lessequals(C,A,t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_36,c_38]) ).
cnf(c_40,plain,
( c_lessequals(A,B,t_b)
| ~ c_less(A,B,t_b) ),
inference(resolve,[status(thm)],[c_36,c_37]) ).
cnf(c_41,plain,
( c_lessequals(B,A,t_b)
| c_less(A,B,t_b) ),
inference(resolve,[status(thm)],[c_29,c_32]) ).
cnf(c_42,plain,
( ~ c_lessequals(B,A,t_b)
| ~ c_less(A,B,t_b) ),
inference(resolve,[status(thm)],[c_29,c_31]) ).
cnf(c_43,plain,
( c_lessequals(c_Orderings_Omax(C,A,t_b),B,t_b)
| ~ c_lessequals(C,B,t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_29,c_30]) ).
cnf(c_44,plain,
c_plus(c_0,A,t_b) = A,
inference(resolve,[status(thm)],[c_24,c_25]) ).
cnf(c_45,plain,
c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b),
inference(resolve,[status(thm)],[c_15,c_20]) ).
cnf(c_46,plain,
c_HOL_Oabs(c_uminus(A,t_b),t_b) = c_HOL_Oabs(A,t_b),
inference(resolve,[status(thm)],[c_15,c_19]) ).
cnf(c_47,plain,
( c_HOL_Oabs(A,t_b) = c_uminus(A,t_b)
| ~ c_lessequals(A,c_0,t_b) ),
inference(resolve,[status(thm)],[c_15,c_18]) ).
cnf(c_48,plain,
( c_uminus(A,t_b) = c_HOL_Oabs(A,t_b)
| ~ c_lessequals(A,c_0,t_b) ),
inference(copy,[status(thm)],[c_47]) ).
fof(cls_conjecture_2,axiom,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_49,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_lessequals(v_g(VAR_0),v_k(VAR_0),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_50,plain,
c_lessequals(v_g(A),v_k(A),t_b),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_51,plain,
c_uminus(c_minus(A,B,t_b),t_b) = c_minus(B,A,t_b),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_52,plain,
c_minus(A,A,t_b) = c_0,
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_53,plain,
c_minus(c_minus(A,B,t_b),C,t_b) = c_minus(A,c_plus(B,C,t_b),t_b),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_55,plain,
c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,B,t_b),C,t_b),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_56,plain,
c_minus(c_plus(A,B,t_b),B,t_b) = A,
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_57,plain,
c_minus(A,B,t_b) = c_plus(A,c_uminus(B,t_b),t_b),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_58,plain,
c_plus(A,c_uminus(B,t_b),t_b) = c_minus(A,B,t_b),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_59,plain,
( c_lessequals(A,C,t_b)
| ~ c_lessequals(c_plus(A,B,t_b),c_plus(C,B,t_b),t_b) ),
inference(resolve,[status(thm)],[c_21,c_22]) ).
cnf(c_60,plain,
( c_lessequals(c_plus(C,A,t_b),c_plus(C,B,t_b),t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_23,c_22]) ).
cnf(c_61,plain,
( c_lessequals(c_minus(A,C,t_b),B,t_b)
| ~ c_lessequals(A,c_plus(B,C,t_b),t_b) ),
inference(resolve,[status(thm)],[c_26,c_27]) ).
cnf(c_62,plain,
( c_less(A,c_plus(C,B,t_b),t_b)
| ~ c_less(c_minus(A,B,t_b),C,t_b) ),
inference(resolve,[status(thm)],[c_28,c_27]) ).
cnf(c_64,plain,
( c_lessequals(B,A,t_b)
| c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_41,c_40]) ).
cnf(c_65,plain,
c_lessequals(A,A,t_b),
inference(factor,[status(thm)],[c_64]) ).
cnf(c_1579,plain,
( c_lessequals(c_Orderings_Omax(A,c_0,t_b),c_HOL_Oabs(B,t_b),t_b)
| ~ c_lessequals(A,c_HOL_Oabs(B,t_b),t_b) ),
inference(resolve,[status(thm)],[c_43,c_45]) ).
cnf(c_71,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(resolve,[status(thm)],[c_1579,c_49]) ).
cnf(c_1580,plain,
( c_lessequals(A,c_HOL_Oabs(B,t_b),t_b)
| ~ c_lessequals(A,c_0,t_b) ),
inference(resolve,[status(thm)],[c_39,c_45]) ).
cnf(c_73,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_0,t_b),
inference(resolve,[status(thm)],[c_1580,c_49]) ).
cnf(c_79,plain,
c_HOL_Oabs(c_minus(A,B,t_b),t_b) = c_HOL_Oabs(c_minus(B,A,t_b),t_b),
inference(paramod,[status(thm)],[c_51,c_46]) ).
cnf(c_1581,plain,
c_uminus(c_minus(A,c_plus(B,C,t_b),t_b),t_b) = c_minus(C,c_minus(A,B,t_b),t_b),
inference(paramod,[status(thm)],[c_53,c_51]) ).
cnf(c_81,plain,
c_minus(c_plus(A,B,t_b),C,t_b) = c_minus(B,c_minus(C,A,t_b),t_b),
inference(paramod,[status(thm)],[c_51,c_1581]) ).
cnf(c_85,plain,
c_minus(A,c_minus(A,B,t_b),t_b) = B,
inference(paramod,[status(thm)],[c_81,c_56]) ).
cnf(c_86,plain,
c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(B,c_minus(C,A,t_b),t_b),
inference(paramod,[status(thm)],[c_81,c_55]) ).
cnf(c_92,plain,
c_lessequals(c_plus(A,v_g(B),t_b),c_plus(A,v_k(B),t_b),t_b),
inference(resolve,[status(thm)],[c_60,c_50]) ).
cnf(c_94,plain,
( c_lessequals(B,c_minus(A,C,t_b),t_b)
| c_less(A,c_plus(B,C,t_b),t_b) ),
inference(resolve,[status(thm)],[c_62,c_41]) ).
cnf(c_102,plain,
( c_uminus(A,t_b) = c_HOL_Oabs(A,t_b)
| c_lessequals(c_0,A,t_b) ),
inference(resolve,[status(thm)],[c_64,c_48]) ).
cnf(c_1582,plain,
( c_lessequals(c_Orderings_Omax(A,B,t_b),B,t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_43,c_65]) ).
cnf(c_114,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),
inference(resolve,[status(thm)],[c_1582,c_73]) ).
cnf(c_1583,plain,
~ c_lessequals(v_f(v_x),c_plus(c_0,v_k(v_x),t_b),t_b),
inference(resolve,[status(thm)],[c_61,c_114]) ).
cnf(c_134,plain,
~ c_lessequals(v_f(v_x),v_k(v_x),t_b),
inference(paramod,[status(thm)],[c_44,c_1583]) ).
cnf(c_1584,plain,
( c_lessequals(A,v_k(B),t_b)
| ~ c_lessequals(A,v_g(B),t_b) ),
inference(resolve,[status(thm)],[c_39,c_50]) ).
cnf(c_142,plain,
~ c_lessequals(v_f(v_x),v_g(v_x),t_b),
inference(resolve,[status(thm)],[c_1584,c_134]) ).
cnf(c_173,plain,
~ c_lessequals(c_plus(v_f(v_x),A,t_b),c_plus(v_g(v_x),A,t_b),t_b),
inference(resolve,[status(thm)],[c_59,c_142]) ).
cnf(c_1585,plain,
~ c_lessequals(c_minus(v_f(v_x),A,t_b),c_plus(v_g(v_x),c_uminus(A,t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_58,c_173]) ).
cnf(c_276,plain,
~ c_lessequals(c_minus(v_f(v_x),A,t_b),c_minus(v_g(v_x),A,t_b),t_b),
inference(paramod,[status(thm)],[c_58,c_1585]) ).
cnf(c_367,plain,
~ c_lessequals(c_0,c_minus(v_g(v_x),v_f(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_52,c_276]) ).
cnf(c_1586,plain,
c_uminus(c_minus(v_g(v_x),v_f(v_x),t_b),t_b) = c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b),
inference(resolve,[status(thm)],[c_367,c_102]) ).
cnf(c_1587,plain,
c_minus(v_f(v_x),v_g(v_x),t_b) = c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_51,c_1586]) ).
cnf(c_370,plain,
c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b) = c_minus(v_f(v_x),v_g(v_x),t_b),
inference(copy,[status(thm)],[c_1587]) ).
cnf(c_1588,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_g(v_x),v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_79,c_71]) ).
cnf(c_474,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_370,c_1588]) ).
cnf(c_1589,plain,
c_plus(A,B,t_b) = c_minus(C,c_minus(c_minus(C,B,t_b),A,t_b),t_b),
inference(paramod,[status(thm)],[c_85,c_86]) ).
cnf(c_1590,plain,
c_plus(A,B,t_b) = c_minus(C,c_minus(C,c_plus(B,A,t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_53,c_1589]) ).
cnf(c_747,plain,
c_plus(A,B,t_b) = c_plus(B,A,t_b),
inference(paramod,[status(thm)],[c_85,c_1590]) ).
cnf(c_1278,plain,
~ c_less(c_plus(A,v_k(B),t_b),c_plus(A,v_g(B),t_b),t_b),
inference(resolve,[status(thm)],[c_92,c_42]) ).
cnf(c_1293,plain,
~ c_less(c_plus(v_k(A),B,t_b),c_plus(B,v_g(A),t_b),t_b),
inference(paramod,[status(thm)],[c_747,c_1278]) ).
cnf(c_1591,plain,
c_lessequals(A,c_minus(c_plus(v_k(B),A,t_b),v_g(B),t_b),t_b),
inference(resolve,[status(thm)],[c_1293,c_94]) ).
cnf(c_1296,plain,
c_lessequals(A,c_minus(A,c_minus(v_g(B),v_k(B),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_81,c_1591]) ).
cnf(c_1592,plain,
~ c_lessequals(v_f(v_x),c_plus(c_minus(v_f(v_x),v_g(v_x),t_b),v_k(v_x),t_b),t_b),
inference(resolve,[status(thm)],[c_61,c_474]) ).
cnf(c_1593,plain,
~ c_lessequals(v_f(v_x),c_plus(v_k(v_x),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_747,c_1592]) ).
cnf(c_1594,plain,
~ c_lessequals(v_f(v_x),c_minus(v_f(v_x),c_minus(v_g(v_x),v_k(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_86,c_1593]) ).
cnf(c_1578,plain,
$false,
inference(resolve,[status(thm)],[c_1296,c_1594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA026-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n019.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 26 22:06:48 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.39 % Process 2291201 was started by sandbox on n019,
% 0.09/0.39 % Sat Sep 26 22:06:48 2026
% 0.09/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 1.47/0.87
% 1.47/0.87 % SZS status Unsatisfiable for theBenchmark
% 1.47/0.87
% 1.47/0.87 % Proof 1 at 0.16 (+ 0.04) seconds.
% 1.47/0.87 % Length of proof is 84.
% 1.47/0.87 % Level of proof is 13.
% 1.47/0.87 % Maximum clause weight is 39.000.
% 1.47/0.87 % Given clauses 222.
% 1.47/0.87
% 1.47/0.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------