TSTP Solution File: ANA034-1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : ANA034-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 17:16:06 EDT 2023
% Result : Unsatisfiable 1779.50s 224.47s
% Output : CNFRefutation 1779.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 54
% Syntax : Number of clauses : 180 ( 87 unt; 4 nHn; 108 RR)
% Number of literals : 303 ( 110 equ; 126 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-3 aty)
% Number of variables : 222 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_less(c_0,v_ca,t_b),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_conjecture_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',tfree_tcs) ).
cnf(cls_OrderedGroup_Onprt__eq__0_0,axiom,
( c_OrderedGroup_Onprt(X2,X1) = c_0
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Onprt__eq__0_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_53,axiom,
( class_OrderedGroup_Olordered__ab__group(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
cnf(cls_OrderedGroup_Onprt__le__zero_0,axiom,
( c_lessequals(c_OrderedGroup_Onprt(X2,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Onprt__le__zero_0) ).
cnf(cls_OrderedGroup_Oabs__of__nonpos_0,axiom,
( c_HOL_Oabs(X2,X1) = c_uminus(X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X2,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(cls_OrderedGroup_Oabs__0__eq_1,axiom,
( c_0 = c_HOL_Oabs(c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Oabs__0__eq_1) ).
cnf(cls_OrderedGroup_Oadd__0__right_0,axiom,
( c_plus(X2,c_0,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Oadd__0__right_0) ).
cnf(cls_OrderedGroup_Odiff__minus__eq__add_0,axiom,
( c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
cnf(clsrel_OrderedGroup_Oab__group__add_1,axiom,
( class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_OrderedGroup_Oab__group__add_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(cls_IntDiv_Ozdiv__1_0,axiom,
c_div(X1,c_1,tc_IntDef_Oint) = X1,
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntDiv_Ozdiv__1_0) ).
cnf(cls_IntDiv_Ozdiv__zmult__self1_0,axiom,
( X1 = c_0
| c_div(c_times(X2,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
cnf(cls_IntDef_Oint__0__neq__1_0,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntDef_Oint__0__neq__1_0) ).
cnf(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
( c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
cnf(cls_Numeral_Omult__minus1_0,axiom,
( c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1)
| ~ class_Numeral_Onumber__ring(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_Numeral_Omult__minus1_0) ).
cnf(clsarity_IntDef__Oint_60,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsarity_IntDef__Oint_60) ).
cnf(cls_OrderedGroup_Oright__minus_0,axiom,
( c_plus(X2,c_uminus(X2,X1),X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Oright__minus_0) ).
cnf(cls_IntDiv_Ozdiv__zminus__zminus_0,axiom,
c_div(c_uminus(X1,tc_IntDef_Oint),c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X1,X2,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
cnf(cls_IntDiv_Ozdiv__minus1__right_0,axiom,
c_div(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X1,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( c_HOL_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
cnf(cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0,axiom,
( c_plus(c_uminus(X2,X1),X2,X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
cnf(cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0,axiom,
c_plus(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X1,X2,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
cnf(clsarity_IntDef__Oint_17,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsarity_IntDef__Oint_17) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_0,axiom,
( class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
cnf(cls_IntDef_Oof__int__diff_0,axiom,
( c_IntDef_Oof__int(c_minus(X2,X3,tc_IntDef_Oint),X1) = c_minus(c_IntDef_Oof__int(X2,X1),c_IntDef_Oof__int(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntDef_Oof__int__diff_0) ).
cnf(cls_IntDiv_ODIVISION__BY__ZERO_0,axiom,
c_Divides_Oop_Amod(X1,c_0,tc_IntDef_Oint) = X1,
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
cnf(cls_IntDiv_Ozmod__zmult__self2_0,axiom,
c_Divides_Oop_Amod(c_times(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_0,
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(cls_IntDef_Oof__int__mult_0,axiom,
( c_IntDef_Oof__int(c_times(X2,X3,tc_IntDef_Oint),X1) = c_times(c_IntDef_Oof__int(X2,X1),c_IntDef_Oof__int(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntDef_Oof__int__mult_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_less(c_0,v_c,t_b),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_conjecture_0) ).
cnf(cls_IntDef_Oof__int__0__eq__iff_1,axiom,
( c_0 = c_IntDef_Oof__int(c_0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
cnf(cls_OrderedGroup_Omult__ac__1_0,axiom,
( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1)
| ~ class_OrderedGroup_Osemigroup__mult(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Omult__ac__1_0) ).
cnf(cls_conjecture_4,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_conjecture_4) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(cls_Ring__and__Field_Omult__cancel__right1_0,axiom,
( X2 = c_0
| X3 = c_1
| ~ class_Ring__and__Field_Oordered__idom(X1)
| X2 != c_times(X3,X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
( class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2,axiom,
( c_lessequals(X2,c_Orderings_Omin(X4,X3,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
cnf(cls_OrderedGroup_Omult__ac__3_0,axiom,
( c_times(X2,c_times(X3,X4,X1),X1) = c_times(X3,c_times(X2,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Omult__ac__3_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(cls_Ring__and__Field_Omult__cancel__right1_2,axiom,
( X2 = c_times(c_1,X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
cnf(cls_Ring__and__Field_Omult__minus__right_0,axiom,
( c_times(X2,c_uminus(X3,X1),X1) = c_uminus(c_times(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_Ring__and__Field_Omult__minus__right_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_3,axiom,
( class_Ring__and__Field_Oring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_conjecture_3) ).
cnf(cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Omin(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
cnf(cls_OrderedGroup_Omult__ac__2_0,axiom,
( c_times(X2,X3,X1) = c_times(X3,X2,X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_OrderedGroup_Omult__ac__2_0) ).
cnf(cls_Ring__and__Field_Omult__mono_0,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X5,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X5,X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_Ring__and__Field_Omult__mono_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_conjecture_2) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',cls_conjecture_5) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( class_Ring__and__Field_Opordered__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
cnf(c_0_54,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
cls_Orderings_Oorder__less__imp__le_0 ).
cnf(c_0_55,negated_conjecture,
c_less(c_0,v_ca,t_b),
cls_conjecture_1 ).
cnf(c_0_56,negated_conjecture,
( c_lessequals(c_0,v_ca,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_57,axiom,
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_44 ).
cnf(c_0_58,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_59,axiom,
( c_OrderedGroup_Onprt(X2,X1) = c_0
| ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X2,X1) ),
cls_OrderedGroup_Onprt__eq__0_0 ).
cnf(c_0_60,negated_conjecture,
c_lessequals(c_0,v_ca,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_61,negated_conjecture,
( c_OrderedGroup_Onprt(v_ca,t_b) = c_0
| ~ class_OrderedGroup_Olordered__ab__group(t_b) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_62,axiom,
( class_OrderedGroup_Olordered__ab__group(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_53 ).
cnf(c_0_63,axiom,
( c_lessequals(c_OrderedGroup_Onprt(X2,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) ),
cls_OrderedGroup_Onprt__le__zero_0 ).
cnf(c_0_64,negated_conjecture,
c_OrderedGroup_Onprt(v_ca,t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_58])]) ).
cnf(c_0_65,negated_conjecture,
( c_lessequals(c_0,c_0,t_b)
| ~ class_OrderedGroup_Olordered__ab__group(t_b) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_66,axiom,
( c_HOL_Oabs(X2,X1) = c_uminus(X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X2,c_0,X1) ),
cls_OrderedGroup_Oabs__of__nonpos_0 ).
cnf(c_0_67,negated_conjecture,
c_lessequals(c_0,c_0,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_62]),c_0_58])]) ).
cnf(c_0_68,negated_conjecture,
( c_HOL_Oabs(c_0,t_b) = c_uminus(c_0,t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_69,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_50 ).
cnf(c_0_70,axiom,
( c_0 = c_HOL_Oabs(c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__0__eq_1 ).
cnf(c_0_71,negated_conjecture,
c_HOL_Oabs(c_0,t_b) = c_uminus(c_0,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_58])]) ).
cnf(c_0_72,axiom,
( c_plus(X2,c_0,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_OrderedGroup_Oadd__0__right_0 ).
cnf(c_0_73,axiom,
( c_minus(X2,c_uminus(X3,X1),X1) = c_plus(X2,X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Odiff__minus__eq__add_0 ).
cnf(c_0_74,axiom,
( class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
clsrel_OrderedGroup_Oab__group__add_1 ).
cnf(c_0_75,negated_conjecture,
( c_uminus(c_0,t_b) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_4 ).
cnf(c_0_77,plain,
( c_minus(X1,c_uminus(c_0,X2),X2) = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_78,negated_conjecture,
c_uminus(c_0,t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_69]),c_0_58])]) ).
cnf(c_0_79,negated_conjecture,
class_OrderedGroup_Oab__group__add(t_b),
inference(spm,[status(thm)],[c_0_76,c_0_58]) ).
cnf(c_0_80,axiom,
c_div(X1,c_1,tc_IntDef_Oint) = X1,
cls_IntDiv_Ozdiv__1_0 ).
cnf(c_0_81,axiom,
( X1 = c_0
| c_div(c_times(X2,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X2 ),
cls_IntDiv_Ozdiv__zmult__self1_0 ).
cnf(c_0_82,axiom,
c_0 != c_1,
cls_IntDef_Oint__0__neq__1_0 ).
cnf(c_0_83,axiom,
( c_uminus(c_minus(X2,X3,X1),X1) = c_minus(X3,X2,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ominus__diff__eq_0 ).
cnf(c_0_84,negated_conjecture,
c_minus(X1,c_0,t_b) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79])]) ).
cnf(c_0_85,axiom,
( c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X2,X1) = c_uminus(X2,X1)
| ~ class_Numeral_Onumber__ring(X1) ),
cls_Numeral_Omult__minus1_0 ).
cnf(c_0_86,plain,
c_times(X1,c_1,tc_IntDef_Oint) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_87,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
clsarity_IntDef__Oint_60 ).
cnf(c_0_88,axiom,
( c_plus(X2,c_uminus(X2,X1),X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Oright__minus_0 ).
cnf(c_0_89,negated_conjecture,
c_minus(c_0,X1,t_b) = c_uminus(X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_79])]) ).
cnf(c_0_90,axiom,
c_div(c_uminus(X1,tc_IntDef_Oint),c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X1,X2,tc_IntDef_Oint),
cls_IntDiv_Ozdiv__zminus__zminus_0 ).
cnf(c_0_91,plain,
c_uminus(c_1,tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
cnf(c_0_92,axiom,
c_div(X1,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X1,tc_IntDef_Oint),
cls_IntDiv_Ozdiv__minus1__right_0 ).
cnf(c_0_93,axiom,
( c_HOL_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X2,X1) ),
cls_OrderedGroup_Oabs__of__nonneg_0 ).
cnf(c_0_94,plain,
( c_minus(X1,c_uminus(c_uminus(X1,X2),X2),X2) = c_0
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_73]) ).
cnf(c_0_95,negated_conjecture,
c_uminus(c_uminus(X1,t_b),t_b) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_89]),c_0_84]),c_0_79])]) ).
cnf(c_0_96,axiom,
( c_plus(c_uminus(X2,X1),X2,X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0 ).
cnf(c_0_97,plain,
c_uminus(c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_80]) ).
cnf(c_0_98,axiom,
c_plus(X1,c_uminus(X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X1,X2,tc_IntDef_Oint),
cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0 ).
cnf(c_0_99,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
clsarity_IntDef__Oint_17 ).
cnf(c_0_100,axiom,
( class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_0 ).
cnf(c_0_101,negated_conjecture,
( c_HOL_Oabs(v_ca,t_b) = v_ca
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_93,c_0_60]) ).
cnf(c_0_102,axiom,
( c_IntDef_Oof__int(c_minus(X2,X3,tc_IntDef_Oint),X1) = c_minus(c_IntDef_Oof__int(X2,X1),c_IntDef_Oof__int(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
cls_IntDef_Oof__int__diff_0 ).
cnf(c_0_103,negated_conjecture,
c_minus(X1,X1,t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_79])]) ).
cnf(c_0_104,plain,
c_minus(X1,X1,tc_IntDef_Oint) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]),c_0_99])]) ).
cnf(c_0_105,negated_conjecture,
class_Ring__and__Field_Ocomm__ring__1(t_b),
inference(spm,[status(thm)],[c_0_100,c_0_58]) ).
cnf(c_0_106,axiom,
c_Divides_Oop_Amod(X1,c_0,tc_IntDef_Oint) = X1,
cls_IntDiv_ODIVISION__BY__ZERO_0 ).
cnf(c_0_107,axiom,
c_Divides_Oop_Amod(c_times(X1,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint) = c_0,
cls_IntDiv_Ozmod__zmult__self2_0 ).
cnf(c_0_108,axiom,
( c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_Ring__and__Field_Oabs__mult_0 ).
cnf(c_0_109,negated_conjecture,
c_HOL_Oabs(v_ca,t_b) = v_ca,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_69]),c_0_58])]) ).
cnf(c_0_110,axiom,
( c_IntDef_Oof__int(c_times(X2,X3,tc_IntDef_Oint),X1) = c_times(c_IntDef_Oof__int(X2,X1),c_IntDef_Oof__int(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
cls_IntDef_Oof__int__mult_0 ).
cnf(c_0_111,negated_conjecture,
c_IntDef_Oof__int(c_0,t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_105])]) ).
cnf(c_0_112,plain,
c_times(c_0,X1,tc_IntDef_Oint) = c_0,
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
c_less(c_0,v_c,t_b),
cls_conjecture_0 ).
cnf(c_0_114,negated_conjecture,
c_times(v_ca,c_HOL_Oabs(X1,t_b),t_b) = c_HOL_Oabs(c_times(v_ca,X1,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_58])]) ).
cnf(c_0_115,negated_conjecture,
c_HOL_Oabs(c_0,t_b) = c_0,
inference(rw,[status(thm)],[c_0_71,c_0_78]) ).
cnf(c_0_116,negated_conjecture,
c_times(c_0,c_IntDef_Oof__int(X1,t_b),t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_111]),c_0_105])]) ).
cnf(c_0_117,axiom,
( c_0 = c_IntDef_Oof__int(c_0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_IntDef_Oof__int__0__eq__iff_1 ).
cnf(c_0_118,axiom,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_21 ).
cnf(c_0_119,negated_conjecture,
( c_lessequals(c_0,v_c,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(spm,[status(thm)],[c_0_54,c_0_113]) ).
cnf(c_0_120,negated_conjecture,
c_HOL_Oabs(c_times(v_ca,c_0,t_b),t_b) = c_times(v_ca,c_0,t_b),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_121,axiom,
( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1)
| ~ class_OrderedGroup_Osemigroup__mult(X1) ),
cls_OrderedGroup_Omult__ac__1_0 ).
cnf(c_0_122,negated_conjecture,
c_times(c_0,c_0,t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_58])]) ).
cnf(c_0_123,negated_conjecture,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(spm,[status(thm)],[c_0_118,c_0_58]) ).
cnf(c_0_124,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
cls_conjecture_4 ).
cnf(c_0_125,negated_conjecture,
c_lessequals(c_0,v_c,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_57]),c_0_58])]) ).
cnf(c_0_126,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__ge__zero_0 ).
cnf(c_0_127,negated_conjecture,
c_HOL_Oabs(c_times(v_ca,c_times(v_ca,c_0,t_b),t_b),t_b) = c_times(v_ca,c_times(v_ca,c_0,t_b),t_b),
inference(spm,[status(thm)],[c_0_114,c_0_120]) ).
cnf(c_0_128,axiom,
( X2 = c_0
| X3 = c_1
| ~ class_Ring__and__Field_Oordered__idom(X1)
| X2 != c_times(X3,X2,X1) ),
cls_Ring__and__Field_Omult__cancel__right1_0 ).
cnf(c_0_129,negated_conjecture,
c_times(c_0,c_times(c_0,X1,t_b),t_b) = c_times(c_0,X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]) ).
cnf(c_0_130,axiom,
( class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_17 ).
cnf(c_0_131,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_121]),c_0_123])]) ).
cnf(c_0_132,negated_conjecture,
( c_HOL_Oabs(v_c,t_b) = v_c
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_93,c_0_125]) ).
cnf(c_0_133,axiom,
( c_lessequals(X2,c_Orderings_Omin(X4,X3,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2 ).
cnf(c_0_134,negated_conjecture,
( c_lessequals(c_0,c_times(v_ca,c_times(v_ca,c_0,t_b),t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_135,axiom,
( c_times(X2,c_times(X3,X4,X1),X1) = c_times(X3,c_times(X2,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_OrderedGroup_Omult__ac__3_0 ).
cnf(c_0_136,negated_conjecture,
c_times(c_0,X1,t_b) = c_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_58])]),c_0_82]) ).
cnf(c_0_137,negated_conjecture,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(spm,[status(thm)],[c_0_130,c_0_58]) ).
cnf(c_0_138,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_33 ).
cnf(c_0_139,negated_conjecture,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(rw,[status(thm)],[c_0_124,c_0_131]) ).
cnf(c_0_140,negated_conjecture,
c_HOL_Oabs(v_c,t_b) = v_c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_69]),c_0_58])]) ).
cnf(c_0_141,plain,
( c_lessequals(c_0,c_Orderings_Omin(c_HOL_Oabs(X1,X2),X3,X2),X2)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(c_0,X3,X2) ),
inference(spm,[status(thm)],[c_0_133,c_0_126]) ).
cnf(c_0_142,negated_conjecture,
c_lessequals(c_0,c_times(v_ca,c_times(v_ca,c_0,t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_69]),c_0_58])]) ).
cnf(c_0_143,negated_conjecture,
c_times(X1,c_0,t_b) = c_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_136]),c_0_137])]) ).
cnf(c_0_144,negated_conjecture,
class_Orderings_Olinorder(t_b),
inference(spm,[status(thm)],[c_0_138,c_0_58]) ).
cnf(c_0_145,negated_conjecture,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_ca,v_g(v_x),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(c_times(v_ca,v_g(v_x),t_b),t_b),t_b),t_b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_114]),c_0_114]) ).
cnf(c_0_146,negated_conjecture,
c_times(v_c,c_HOL_Oabs(X1,t_b),t_b) = c_HOL_Oabs(c_times(v_c,X1,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_140]),c_0_58])]) ).
cnf(c_0_147,axiom,
( X2 = c_times(c_1,X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_Ring__and__Field_Omult__cancel__right1_2 ).
cnf(c_0_148,axiom,
( c_times(X2,c_uminus(X3,X1),X1) = c_uminus(c_times(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_Ring__and__Field_Omult__minus__right_0 ).
cnf(c_0_149,axiom,
( class_Ring__and__Field_Oring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_3 ).
cnf(c_0_150,negated_conjecture,
( c_lessequals(c_0,c_Orderings_Omin(c_HOL_Oabs(X1,t_b),c_0,t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]),c_0_143]),c_0_144])]) ).
cnf(c_0_151,negated_conjecture,
c_times(c_HOL_Oabs(c_times(v_c,v_f(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_ca,v_g(v_x),t_b),t_b),t_b) = c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(c_times(v_ca,v_g(v_x),t_b),t_b),t_b),t_b),
inference(rw,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_152,negated_conjecture,
c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(c_times(v_ca,v_g(v_x),t_b),t_b),t_b),t_b) = c_HOL_Oabs(c_times(v_c,c_times(v_ca,c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_131]),c_0_123])]),c_0_114]),c_0_114]),c_0_146]) ).
cnf(c_0_153,plain,
( c_uminus(c_times(c_1,X1,X2),X2) = c_uminus(X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149]) ).
cnf(c_0_154,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
cls_conjecture_3 ).
cnf(c_0_155,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,c_Orderings_Omin(X3,X4,X1),X1) ),
cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0 ).
cnf(c_0_156,negated_conjecture,
c_lessequals(c_0,c_Orderings_Omin(c_HOL_Oabs(X1,t_b),c_0,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_69]),c_0_58])]) ).
cnf(c_0_157,negated_conjecture,
c_times(c_HOL_Oabs(c_times(v_c,v_f(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_ca,v_g(v_x),t_b),t_b),t_b) = c_HOL_Oabs(c_times(v_c,c_times(v_ca,c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(rw,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_158,plain,
( c_times(c_HOL_Oabs(X1,X2),c_times(X3,c_HOL_Oabs(X4,X2),X2),X2) = c_times(X3,c_HOL_Oabs(c_times(X1,X4,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_108]),c_0_130]) ).
cnf(c_0_159,axiom,
( c_times(X2,X3,X1) = c_times(X3,X2,X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_OrderedGroup_Omult__ac__2_0 ).
cnf(c_0_160,negated_conjecture,
c_times(c_1,X1,t_b) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_153]),c_0_95]),c_0_58])]) ).
cnf(c_0_161,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X5,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X5,X1) ),
cls_Ring__and__Field_Omult__mono_0 ).
cnf(c_0_162,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(c_times(v_ca,v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[c_0_154,c_0_114]) ).
cnf(c_0_163,negated_conjecture,
c_times(c_HOL_Oabs(c_times(v_ca,X1,t_b),t_b),X2,t_b) = c_times(v_ca,c_times(c_HOL_Oabs(X1,t_b),X2,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_114]),c_0_123])]) ).
cnf(c_0_164,negated_conjecture,
c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_144])]) ).
cnf(c_0_165,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
cls_conjecture_2 ).
cnf(c_0_166,negated_conjecture,
c_times(v_ca,c_times(c_HOL_Oabs(c_times(v_c,v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_HOL_Oabs(c_times(v_c,c_times(v_ca,c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_109]),c_0_58])]) ).
cnf(c_0_167,negated_conjecture,
c_times(X1,c_1,t_b) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_137])]) ).
cnf(c_0_168,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
cls_conjecture_5 ).
cnf(c_0_169,negated_conjecture,
( c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),X1,t_b),c_times(v_ca,c_times(c_HOL_Oabs(v_g(v_x),t_b),X2,t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ c_lessequals(X1,X2,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]),c_0_164])]) ).
cnf(c_0_170,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(c_times(v_c,v_f(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[c_0_165,c_0_146]) ).
cnf(c_0_171,negated_conjecture,
c_times(v_ca,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(c_times(v_c,v_f(v_x),t_b),t_b),t_b),t_b) = c_HOL_Oabs(c_times(v_c,c_times(v_ca,c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_159]),c_0_137])]) ).
cnf(c_0_172,negated_conjecture,
c_times(X1,X2,t_b) = c_times(X2,X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_167]),c_0_167]),c_0_137])]) ).
cnf(c_0_173,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_121]),c_0_123])]) ).
cnf(c_0_174,negated_conjecture,
( c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_c,c_times(v_ca,c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_171]),c_0_164])]),c_0_172]) ).
cnf(c_0_175,axiom,
( class_Ring__and__Field_Opordered__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_42 ).
cnf(c_0_176,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(v_c,c_HOL_Oabs(c_times(v_ca,c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),t_b),
inference(spm,[status(thm)],[c_0_173,c_0_114]) ).
cnf(c_0_177,negated_conjecture,
c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_c,c_times(v_ca,c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_58])]) ).
cnf(c_0_178,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_HOL_Oabs(c_times(v_c,c_times(v_ca,c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),t_b),
inference(rw,[status(thm)],[c_0_176,c_0_146]) ).
cnf(c_0_179,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_108]),c_0_58])]),c_0_178]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.33 % Problem : ANA034-1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.34 % Command : run_E %s %d THM
% 0.36/0.55 % Computer : n010.cluster.edu
% 0.36/0.55 % Model : x86_64 x86_64
% 0.36/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.36/0.55 % Memory : 8042.1875MB
% 0.36/0.55 % OS : Linux 3.10.0-693.el7.x86_64
% 0.36/0.55 % CPULimit : 2400
% 0.36/0.55 % WCLimit : 300
% 0.36/0.55 % DateTime : Mon Oct 2 14:55:05 EDT 2023
% 0.36/0.55 % CPUTime :
% 0.40/0.93 Running first-order theorem proving
% 0.40/0.93 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.EQ2TEqxz01/E---3.1_26084.p
% 1779.50/224.47 # Version: 3.1pre001
% 1779.50/224.47 # Preprocessing class: FMLMSMSMSSSNFFN.
% 1779.50/224.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1779.50/224.47 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1779.50/224.47 # Starting new_bool_3 with 300s (1) cores
% 1779.50/224.47 # Starting new_bool_1 with 300s (1) cores
% 1779.50/224.47 # Starting sh5l with 300s (1) cores
% 1779.50/224.47 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 26244 completed with status 0
% 1779.50/224.47 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1779.50/224.47 # Preprocessing class: FMLMSMSMSSSNFFN.
% 1779.50/224.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1779.50/224.47 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1779.50/224.47 # No SInE strategy applied
% 1779.50/224.47 # Search class: FGHSM-SMLM32-DFFFFFNN
% 1779.50/224.47 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 1779.50/224.47 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 1779.50/224.47 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1779.50/224.47 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 1779.50/224.47 # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 1779.50/224.47 # Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 113s (1) cores
% 1779.50/224.47 # G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with pid 26253 completed with status 7
% 1779.50/224.47 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 113s (1) cores
% 1779.50/224.47 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with pid 26251 completed with status 7
% 1779.50/224.47 # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 113s (1) cores
% 1779.50/224.47 # G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 26254 completed with status 7
% 1779.50/224.47 # Starting U----_206c_02_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 1779.50/224.47 # G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with pid 26255 completed with status 7
% 1779.50/224.47 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 113s (1) cores
% 1779.50/224.47 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 26252 completed with status 7
% 1779.50/224.47 # Starting G-E--_107_C41_F1_PI_AE_Q4_CS_SP_PS_S0Y with 113s (1) cores
% 1779.50/224.47 # G-E--_200_B02_F1_SE_CS_SP_PI_S2k with pid 30686 completed with status 0
% 1779.50/224.47 # Result found by G-E--_200_B02_F1_SE_CS_SP_PI_S2k
% 1779.50/224.47 # Preprocessing class: FMLMSMSMSSSNFFN.
% 1779.50/224.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1779.50/224.47 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1779.50/224.47 # No SInE strategy applied
% 1779.50/224.47 # Search class: FGHSM-SMLM32-DFFFFFNN
% 1779.50/224.47 # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 1779.50/224.47 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 113s (1) cores
% 1779.50/224.47 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1779.50/224.47 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 1779.50/224.47 # Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 1779.50/224.47 # Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 113s (1) cores
% 1779.50/224.47 # G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with pid 26253 completed with status 7
% 1779.50/224.47 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 113s (1) cores
% 1779.50/224.47 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with pid 26251 completed with status 7
% 1779.50/224.47 # Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 113s (1) cores
% 1779.50/224.47 # Preprocessing time : 0.017 s
% 1779.50/224.47
% 1779.50/224.47 # Proof found!
% 1779.50/224.47 # SZS status Unsatisfiable
% 1779.50/224.47 # SZS output start CNFRefutation
% See solution above
% 1779.50/224.47 # Parsed axioms : 2796
% 1779.50/224.47 # Removed by relevancy pruning/SinE : 0
% 1779.50/224.47 # Initial clauses : 2796
% 1779.50/224.47 # Removed in clause preprocessing : 9
% 1779.50/224.47 # Initial clauses in saturation : 2787
% 1779.50/224.47 # Processed clauses : 169023
% 1779.50/224.47 # ...of these trivial : 11425
% 1779.50/224.47 # ...subsumed : 122099
% 1779.50/224.47 # ...remaining for further processing : 35499
% 1779.50/224.47 # Other redundant clauses eliminated : 9303
% 1779.50/224.47 # Clauses deleted for lack of memory : 364267
% 1779.50/224.47 # Backward-subsumed : 1308
% 1779.50/224.47 # Backward-rewritten : 12413
% 1779.50/224.47 # Generated clauses : 3597865
% 1779.50/224.47 # ...of the previous two non-redundant : 3154512
% 1779.50/224.47 # ...aggressively subsumed : 0
% 1779.50/224.47 # Contextual simplify-reflections : 2585
% 1779.50/224.47 # Paramodulations : 3588293
% 1779.50/224.47 # Factorizations : 46
% 1779.50/224.47 # NegExts : 0
% 1779.50/224.47 # Equation resolutions : 9526
% 1779.50/224.47 # Total rewrite steps : 3578953
% 1779.50/224.47 # Propositional unsat checks : 0
% 1779.50/224.47 # Propositional check models : 0
% 1779.50/224.47 # Propositional check unsatisfiable : 0
% 1779.50/224.47 # Propositional clauses : 0
% 1779.50/224.47 # Propositional clauses after purity: 0
% 1779.50/224.47 # Propositional unsat core size : 0
% 1779.50/224.47 # Propositional preprocessing time : 0.000
% 1779.50/224.47 # Propositional encoding time : 0.000
% 1779.50/224.47 # Propositional solver time : 0.000
% 1779.50/224.47 # Success case prop preproc time : 0.000
% 1779.50/224.47 # Success case prop encoding time : 0.000
% 1779.50/224.47 # Success case prop solver time : 0.000
% 1779.50/224.47 # Current number of processed clauses : 21778
% 1779.50/224.47 # Positive orientable unit clauses : 4539
% 1779.50/224.47 # Positive unorientable unit clauses: 156
% 1779.50/224.47 # Negative unit clauses : 1403
% 1779.50/224.47 # Non-unit-clauses : 15680
% 1779.50/224.47 # Current number of unprocessed clauses: 1021378
% 1779.50/224.47 # ...number of literals in the above : 3297487
% 1779.50/224.47 # Current number of archived formulas : 0
% 1779.50/224.47 # Current number of archived clauses : 13729
% 1779.50/224.47 # Clause-clause subsumption calls (NU) : 86663934
% 1779.50/224.47 # Rec. Clause-clause subsumption calls : 41691116
% 1779.50/224.47 # Non-unit clause-clause subsumptions : 69213
% 1779.50/224.47 # Unit Clause-clause subsumption calls : 2480774
% 1779.50/224.47 # Rewrite failures with RHS unbound : 584
% 1779.50/224.47 # BW rewrite match attempts : 925511
% 1779.50/224.47 # BW rewrite match successes : 12419
% 1779.50/224.47 # Condensation attempts : 0
% 1779.50/224.47 # Condensation successes : 0
% 1779.50/224.47 # Termbank termtop insertions : 92598280
% 1779.50/224.47
% 1779.50/224.47 # -------------------------------------------------
% 1779.50/224.47 # User time : 703.332 s
% 1779.50/224.47 # System time : 9.579 s
% 1779.50/224.47 # Total time : 712.912 s
% 1779.50/224.47 # Maximum resident set size: 6444 pages
% 1779.50/224.47
% 1779.50/224.47 # -------------------------------------------------
% 1779.50/224.47 # User time : 1095.555 s
% 1779.50/224.47 # System time : 16.080 s
% 1779.50/224.47 # Total time : 1111.635 s
% 1779.50/224.47 # Maximum resident set size: 3520 pages
% 1779.50/224.47 % E---3.1 exiting
% 1779.50/224.47 % E---3.1 exiting
%------------------------------------------------------------------------------