%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 : Tue Sep 29 09:30:57 AM UTC 2026
% Result : Unsatisfiable 1.09s 1.16s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 45
% Syntax : Number of formulae : 250 ( 67 unt; 28 def)
% Number of atoms : 734 ( 168 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 948 ( 464 ~; 456 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 145 ( 0 sgn 145 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X2,X0,X1] : ifeq2(class_Ring__and__Field_Oordered__idom(X0),true,c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),c_HOL_Oabs(c_times(X1,X2,X0),X0)) = c_HOL_Oabs(c_times(X1,X2,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f4,plain,
! [X2,X0,X1] : c_HOL_Oabs(c_times(X1,X2,X0),X0) = ifeq2(class_Ring__and__Field_Oordered__idom(X0),true,c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),c_HOL_Oabs(c_times(X1,X2,X0),X0)),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X2,X3,X0,X1,X4] : ifeq(c_lessequals(c_0,X0,X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(X3,X0,X1),true,ifeq(c_lessequals(X2,X4,X1),true,ifeq(class_Ring__and__Field_Opordered__semiring(X1),true,c_lessequals(c_times(X3,X2,X1),c_times(X0,X4,X1),X1),true),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
fof(f6,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(c_lessequals(c_0,X0,X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(X3,X0,X1),true,ifeq(c_lessequals(X2,X4,X1),true,ifeq(class_Ring__and__Field_Opordered__semiring(X1),true,c_lessequals(c_times(X3,X2,X1),c_times(X0,X4,X1),X1),true),true),true),true),true),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),true,ifeq(c_lessequals(c_0,X1,X0),true,ifeq(c_lessequals(c_0,X2,X0),true,c_lessequals(c_0,c_times(X1,X2,X0),X0),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f8,plain,
! [X2,X0,X1] : true = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),true,ifeq(c_lessequals(c_0,X1,X0),true,ifeq(c_lessequals(c_0,X2,X0),true,c_lessequals(c_0,c_times(X1,X2,X0),X0),true),true),true),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X2,X0,X1] : ifeq(c_less(X0,X1,X2),true,ifeq(class_Orderings_Oorder(X2),true,c_lessequals(X0,X1,X2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f10,plain,
! [X2,X0,X1] : true = ifeq(c_less(X0,X1,X2),true,ifeq(class_Orderings_Oorder(X2),true,c_lessequals(X0,X1,X2),true),true),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0,X1] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f12,plain,
! [X0,X1] : true = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),true),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
c_less(c_0,v_c,t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f14,plain,
true = c_less(c_0,v_c,t_b),
inference(reorient_equations,[],[f13]) ).
fof(f15,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) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f16,plain,
true = 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),
inference(reorient_equations,[],[f15]) ).
fof(f17,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) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f18,plain,
true = 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),
inference(reorient_equations,[],[f17]) ).
fof(f19,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/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f20,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) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f21,plain,
true != 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),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f23,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X0] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,class_Orderings_Oorder(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f25,plain,
! [X0] : true = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,class_Orderings_Oorder(X0),true),
inference(reorient_equations,[],[f24]) ).
fof(f26,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__cancel__semiring(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f27,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__cancel__semiring(X0),true),
inference(reorient_equations,[],[f26]) ).
fof(f28,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__semiring(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f29,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__semiring(X0),true),
inference(reorient_equations,[],[f28]) ).
fof(f30,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Olordered__ab__group__abs(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f31,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Olordered__ab__group__abs(X0),true),
inference(reorient_equations,[],[f30]) ).
fof(f33,definition,
( spl0_1
<=> true = class_Ring__and__Field_Oordered__idom(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f35,plain,
( true = class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
spl0_1,
inference(avatar_split_clause,[],[f23,f33]) ).
fof(f38,definition,
( spl0_2
<=> true = 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) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f40,plain,
( true != 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)
| spl0_2 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f21,f38]) ).
fof(f43,definition,
( spl0_3
<=> 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) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f45,plain,
( 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)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,plain,
spl0_3,
inference(avatar_split_clause,[],[f19,f43]) ).
fof(f48,definition,
( spl0_4
<=> true = 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) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f50,plain,
( true = 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)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
spl0_4,
inference(avatar_split_clause,[],[f18,f48]) ).
fof(f53,definition,
( spl0_5
<=> true = 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) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f55,plain,
( true = 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)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
spl0_5,
inference(avatar_split_clause,[],[f16,f53]) ).
fof(f58,definition,
( spl0_6
<=> true = c_less(c_0,v_c,t_b) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f60,plain,
( true = c_less(c_0,v_c,t_b)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
spl0_6,
inference(avatar_split_clause,[],[f14,f58]) ).
fof(f62,plain,
( ! [X2,X0,X1] : c_HOL_Oabs(c_times(X1,X2,X0),X0) = ifeq2(class_Ring__and__Field_Oordered__idom(X0),class_Ring__and__Field_Oordered__idom(t_b),c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),c_HOL_Oabs(c_times(X1,X2,X0),X0))
| ~ spl0_1 ),
inference(backward_demodulation,[],[f4,f35]) ).
fof(f63,plain,
( ! [X2,X3,X0,X1,X4] : class_Ring__and__Field_Oordered__idom(t_b) = ifeq(c_lessequals(c_0,X0,X1),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,X2,X1),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X3,X0,X1),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(X2,X4,X1),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(X1),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_times(X3,X2,X1),c_times(X0,X4,X1),X1),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b))
| ~ spl0_1 ),
inference(backward_demodulation,[],[f6,f35]) ).
fof(f64,plain,
( ! [X2,X0,X1] : class_Ring__and__Field_Oordered__idom(t_b) = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,X1,X0),class_Ring__and__Field_Oordered__idom(t_b),ifeq(c_lessequals(c_0,X2,X0),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_times(X1,X2,X0),X0),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b))
| ~ spl0_1 ),
inference(backward_demodulation,[],[f8,f35]) ).
fof(f65,plain,
( ! [X2,X0,X1] : class_Ring__and__Field_Oordered__idom(t_b) = ifeq(c_less(X0,X1,X2),class_Ring__and__Field_Oordered__idom(t_b),ifeq(class_Orderings_Oorder(X2),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(X0,X1,X2),class_Ring__and__Field_Oordered__idom(t_b)),class_Ring__and__Field_Oordered__idom(t_b))
| ~ spl0_1 ),
inference(backward_demodulation,[],[f10,f35]) ).
fof(f66,plain,
( ! [X0,X1] : class_Ring__and__Field_Oordered__idom(t_b) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),class_Ring__and__Field_Oordered__idom(t_b),c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),class_Ring__and__Field_Oordered__idom(t_b))
| ~ spl0_1 ),
inference(backward_demodulation,[],[f12,f35]) ).
fof(f67,plain,
( ! [X0] : class_Ring__and__Field_Oordered__idom(t_b) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),class_Ring__and__Field_Oordered__idom(t_b),class_Orderings_Oorder(X0),class_Ring__and__Field_Oordered__idom(t_b))
| ~ spl0_1 ),
inference(backward_demodulation,[],[f25,f35]) ).
fof(f68,plain,
( ! [X0] : class_Ring__and__Field_Oordered__idom(t_b) = ifeq(class_Ring__and__Field_Oordered__idom(X0),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__cancel__semiring(X0),class_Ring__and__Field_Oordered__idom(t_b))
| ~ spl0_1 ),
inference(backward_demodulation,[],[f27,f35]) ).
fof(f69,plain,
( ! [X0] : class_Ring__and__Field_Oordered__idom(t_b) = ifeq(class_Ring__and__Field_Oordered__idom(X0),class_Ring__and__Field_Oordered__idom(t_b),class_Ring__and__Field_Opordered__semiring(X0),class_Ring__and__Field_Oordered__idom(t_b))
| ~ spl0_1 ),
inference(backward_demodulation,[],[f29,f35]) ).
fof(f70,plain,
( ! [X0] : class_Ring__and__Field_Oordered__idom(t_b) = ifeq(class_Ring__and__Field_Oordered__idom(X0),class_Ring__and__Field_Oordered__idom(t_b),class_OrderedGroup_Olordered__ab__group__abs(X0),class_Ring__and__Field_Oordered__idom(t_b))
| ~ spl0_1 ),
inference(backward_demodulation,[],[f31,f35]) ).
fof(f71,plain,
( 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) != class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_1
| spl0_2 ),
inference(forward_demodulation,[],[f40,f35]) ).
fof(f72,plain,
( 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) = class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f50,f35]) ).
fof(f73,plain,
( 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) = class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f55,f35]) ).
fof(f74,plain,
( c_less(c_0,v_c,t_b) = class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f60,f35]) ).
fof(f76,definition,
( spl0_7
<=> 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) = class_Ring__and__Field_Oordered__idom(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f78,plain,
( 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) != class_Ring__and__Field_Oordered__idom(t_b)
| spl0_7 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( ~ spl0_7
| ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f71,f38,f33,f76]) ).
fof(f81,definition,
( spl0_8
<=> 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) = class_Ring__and__Field_Oordered__idom(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f83,plain,
( 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) = class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl0_8
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f72,f48,f33,f81]) ).
fof(f86,definition,
( spl0_9
<=> 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) = class_Ring__and__Field_Oordered__idom(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f88,plain,
( 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) = class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( spl0_9
| ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f73,f53,f33,f86]) ).
fof(f91,definition,
( spl0_10
<=> c_less(c_0,v_c,t_b) = class_Ring__and__Field_Oordered__idom(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f93,plain,
( c_less(c_0,v_c,t_b) = class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_10
| ~ spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f74,f58,f33,f91]) ).
fof(f96,plain,
( ! [X2,X0,X1] : c_HOL_Oabs(c_times(X1,X2,X0),X0) = ifeq2(class_Ring__and__Field_Oordered__idom(X0),c_less(c_0,v_c,t_b),c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),c_HOL_Oabs(c_times(X1,X2,X0),X0))
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[],[f62,f93]) ).
fof(f97,plain,
( ! [X2,X3,X0,X1,X4] : c_less(c_0,v_c,t_b) = ifeq(c_lessequals(c_0,X0,X1),c_less(c_0,v_c,t_b),ifeq(c_lessequals(c_0,X2,X1),c_less(c_0,v_c,t_b),ifeq(c_lessequals(X3,X0,X1),c_less(c_0,v_c,t_b),ifeq(c_lessequals(X2,X4,X1),c_less(c_0,v_c,t_b),ifeq(class_Ring__and__Field_Opordered__semiring(X1),c_less(c_0,v_c,t_b),c_lessequals(c_times(X3,X2,X1),c_times(X0,X4,X1),X1),c_less(c_0,v_c,t_b)),c_less(c_0,v_c,t_b)),c_less(c_0,v_c,t_b)),c_less(c_0,v_c,t_b)),c_less(c_0,v_c,t_b))
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[],[f63,f93]) ).
fof(f98,plain,
( ! [X2,X0,X1] : c_less(c_0,v_c,t_b) = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),c_less(c_0,v_c,t_b),ifeq(c_lessequals(c_0,X1,X0),c_less(c_0,v_c,t_b),ifeq(c_lessequals(c_0,X2,X0),c_less(c_0,v_c,t_b),c_lessequals(c_0,c_times(X1,X2,X0),X0),c_less(c_0,v_c,t_b)),c_less(c_0,v_c,t_b)),c_less(c_0,v_c,t_b))
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[],[f64,f93]) ).
fof(f99,plain,
( ! [X2,X0,X1] : c_less(c_0,v_c,t_b) = ifeq(c_less(X0,X1,X2),c_less(c_0,v_c,t_b),ifeq(class_Orderings_Oorder(X2),c_less(c_0,v_c,t_b),c_lessequals(X0,X1,X2),c_less(c_0,v_c,t_b)),c_less(c_0,v_c,t_b))
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[],[f65,f93]) ).
fof(f100,plain,
( ! [X0,X1] : c_less(c_0,v_c,t_b) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),c_less(c_0,v_c,t_b),c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),c_less(c_0,v_c,t_b))
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[],[f66,f93]) ).
fof(f101,plain,
( ! [X0] : c_less(c_0,v_c,t_b) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),c_less(c_0,v_c,t_b),class_Orderings_Oorder(X0),c_less(c_0,v_c,t_b))
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[],[f67,f93]) ).
fof(f102,plain,
( ! [X0] : c_less(c_0,v_c,t_b) = ifeq(class_Ring__and__Field_Oordered__idom(X0),c_less(c_0,v_c,t_b),class_Ring__and__Field_Opordered__cancel__semiring(X0),c_less(c_0,v_c,t_b))
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[],[f68,f93]) ).
fof(f103,plain,
( ! [X0] : c_less(c_0,v_c,t_b) = ifeq(class_Ring__and__Field_Oordered__idom(X0),c_less(c_0,v_c,t_b),class_Ring__and__Field_Opordered__semiring(X0),c_less(c_0,v_c,t_b))
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[],[f69,f93]) ).
fof(f104,plain,
( ! [X0] : c_less(c_0,v_c,t_b) = ifeq(class_Ring__and__Field_Oordered__idom(X0),c_less(c_0,v_c,t_b),class_OrderedGroup_Olordered__ab__group__abs(X0),c_less(c_0,v_c,t_b))
| ~ spl0_1
| ~ spl0_10 ),
inference(backward_demodulation,[],[f70,f93]) ).
fof(f105,plain,
( c_less(c_0,v_c,t_b) != 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)
| spl0_7
| ~ spl0_10 ),
inference(backward_demodulation,[],[f78,f93]) ).
fof(f106,plain,
( c_less(c_0,v_c,t_b) = 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)
| ~ spl0_8
| ~ spl0_10 ),
inference(backward_demodulation,[],[f83,f93]) ).
fof(f107,plain,
( c_less(c_0,v_c,t_b) = 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)
| ~ spl0_9
| ~ spl0_10 ),
inference(backward_demodulation,[],[f88,f93]) ).
fof(f109,definition,
( spl0_11
<=> c_less(c_0,v_c,t_b) = 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) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( c_less(c_0,v_c,t_b) = 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)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f107,f91,f86,f109]) ).
fof(f114,definition,
( spl0_12
<=> c_less(c_0,v_c,t_b) = 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) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f116,plain,
( c_less(c_0,v_c,t_b) = 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)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_12
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f106,f91,f81,f114]) ).
fof(f119,definition,
( spl0_13
<=> c_less(c_0,v_c,t_b) = 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) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f121,plain,
( c_less(c_0,v_c,t_b) != 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)
| spl0_13 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( ~ spl0_13
| spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f105,f91,f76,f119]) ).
fof(f124,plain,
( c_less(c_0,v_c,t_b) = ifeq(c_less(c_0,v_c,t_b),c_less(c_0,v_c,t_b),class_Ring__and__Field_Opordered__cancel__semiring(t_b),c_less(c_0,v_c,t_b))
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[],[f102,f93]) ).
fof(f125,plain,
( c_less(c_0,v_c,t_b) = class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_1
| ~ spl0_10 ),
inference(forward_demodulation,[],[f124,f2]) ).
fof(f127,definition,
( spl0_14
<=> c_less(c_0,v_c,t_b) = class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f129,plain,
( c_less(c_0,v_c,t_b) = class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f130,plain,
( spl0_14
| ~ spl0_1
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f125,f91,f33,f127]) ).
fof(f132,plain,
( class_Ring__and__Field_Oordered__idom(t_b) = class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f93,f129]) ).
fof(f133,plain,
( ! [X2,X0,X1] : c_HOL_Oabs(c_times(X1,X2,X0),X0) = ifeq2(class_Ring__and__Field_Oordered__idom(X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b),c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),c_HOL_Oabs(c_times(X1,X2,X0),X0))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f96,f129]) ).
fof(f134,plain,
( ! [X2,X3,X0,X1,X4] : class_Ring__and__Field_Opordered__cancel__semiring(t_b) = ifeq(c_lessequals(c_0,X0,X1),class_Ring__and__Field_Opordered__cancel__semiring(t_b),ifeq(c_lessequals(c_0,X2,X1),class_Ring__and__Field_Opordered__cancel__semiring(t_b),ifeq(c_lessequals(X3,X0,X1),class_Ring__and__Field_Opordered__cancel__semiring(t_b),ifeq(c_lessequals(X2,X4,X1),class_Ring__and__Field_Opordered__cancel__semiring(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(X1),class_Ring__and__Field_Opordered__cancel__semiring(t_b),c_lessequals(c_times(X3,X2,X1),c_times(X0,X4,X1),X1),class_Ring__and__Field_Opordered__cancel__semiring(t_b)),class_Ring__and__Field_Opordered__cancel__semiring(t_b)),class_Ring__and__Field_Opordered__cancel__semiring(t_b)),class_Ring__and__Field_Opordered__cancel__semiring(t_b)),class_Ring__and__Field_Opordered__cancel__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f97,f129]) ).
fof(f135,plain,
( ! [X2,X0,X1] : class_Ring__and__Field_Opordered__cancel__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b),ifeq(c_lessequals(c_0,X1,X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b),ifeq(c_lessequals(c_0,X2,X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b),c_lessequals(c_0,c_times(X1,X2,X0),X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b)),class_Ring__and__Field_Opordered__cancel__semiring(t_b)),class_Ring__and__Field_Opordered__cancel__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f98,f129]) ).
fof(f136,plain,
( ! [X2,X0,X1] : class_Ring__and__Field_Opordered__cancel__semiring(t_b) = ifeq(c_less(X0,X1,X2),class_Ring__and__Field_Opordered__cancel__semiring(t_b),ifeq(class_Orderings_Oorder(X2),class_Ring__and__Field_Opordered__cancel__semiring(t_b),c_lessequals(X0,X1,X2),class_Ring__and__Field_Opordered__cancel__semiring(t_b)),class_Ring__and__Field_Opordered__cancel__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f99,f129]) ).
fof(f137,plain,
( ! [X0,X1] : class_Ring__and__Field_Opordered__cancel__semiring(t_b) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b),c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f100,f129]) ).
fof(f138,plain,
( ! [X0] : class_Ring__and__Field_Opordered__cancel__semiring(t_b) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b),class_Orderings_Oorder(X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f101,f129]) ).
fof(f140,plain,
( ! [X0] : class_Ring__and__Field_Opordered__cancel__semiring(t_b) = ifeq(class_Ring__and__Field_Oordered__idom(X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b),class_Ring__and__Field_Opordered__semiring(X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f103,f129]) ).
fof(f141,plain,
( ! [X0] : class_Ring__and__Field_Opordered__cancel__semiring(t_b) = ifeq(class_Ring__and__Field_Oordered__idom(X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b),class_OrderedGroup_Olordered__ab__group__abs(X0),class_Ring__and__Field_Opordered__cancel__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14 ),
inference(backward_demodulation,[],[f104,f129]) ).
fof(f142,plain,
( 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) = class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_11
| ~ spl0_14 ),
inference(backward_demodulation,[],[f111,f129]) ).
fof(f143,plain,
( 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) = class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_12
| ~ spl0_14 ),
inference(backward_demodulation,[],[f116,f129]) ).
fof(f144,plain,
( 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) != class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| spl0_13
| ~ spl0_14 ),
inference(backward_demodulation,[],[f121,f129]) ).
fof(f146,definition,
( spl0_15
<=> 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) = class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f148,plain,
( 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) != class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| spl0_15 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( ~ spl0_15
| spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f144,f127,f119,f146]) ).
fof(f151,definition,
( spl0_16
<=> 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) = class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f153,plain,
( 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) = class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_16
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f143,f127,f114,f151]) ).
fof(f156,definition,
( spl0_17
<=> 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) = class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f158,plain,
( 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) = class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,plain,
( spl0_17
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f142,f127,f109,f156]) ).
fof(f161,definition,
( spl0_18
<=> class_Ring__and__Field_Oordered__idom(t_b) = class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f163,plain,
( class_Ring__and__Field_Oordered__idom(t_b) = class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( spl0_18
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f132,f127,f91,f161]) ).
fof(f171,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),class_Ring__and__Field_Opordered__cancel__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__cancel__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_18 ),
inference(superposition,[],[f140,f163]) ).
fof(f172,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(t_b) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f171,f2]) ).
fof(f174,definition,
( spl0_20
<=> class_Ring__and__Field_Opordered__cancel__semiring(t_b) = class_Ring__and__Field_Opordered__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f176,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(t_b) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( spl0_20
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f172,f161,f127,f91,f33,f174]) ).
fof(f178,plain,
( c_less(c_0,v_c,t_b) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f129,f176]) ).
fof(f179,plain,
( ! [X2,X0,X1] : c_HOL_Oabs(c_times(X1,X2,X0),X0) = ifeq2(class_Ring__and__Field_Oordered__idom(X0),class_Ring__and__Field_Opordered__semiring(t_b),c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),c_HOL_Oabs(c_times(X1,X2,X0),X0))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f133,f176]) ).
fof(f180,plain,
( ! [X2,X3,X0,X1,X4] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,X0,X1),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(c_0,X2,X1),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(X3,X0,X1),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(X2,X4,X1),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(X1),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_times(X3,X2,X1),c_times(X0,X4,X1),X1),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f134,f176]) ).
fof(f181,plain,
( ! [X2,X0,X1] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(c_0,X1,X0),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(c_0,X2,X0),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,c_times(X1,X2,X0),X0),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f135,f176]) ).
fof(f182,plain,
( ! [X2,X0,X1] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_less(X0,X1,X2),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(class_Orderings_Oorder(X2),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(X0,X1,X2),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f136,f176]) ).
fof(f183,plain,
( ! [X0,X1] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f137,f176]) ).
fof(f184,plain,
( ! [X0] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),class_Ring__and__Field_Opordered__semiring(t_b),class_Orderings_Oorder(X0),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f138,f176]) ).
fof(f187,plain,
( ! [X0] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Oordered__idom(X0),class_Ring__and__Field_Opordered__semiring(t_b),class_OrderedGroup_Olordered__ab__group__abs(X0),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[],[f141,f176]) ).
fof(f188,plain,
( 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) != class_Ring__and__Field_Opordered__semiring(t_b)
| spl0_15
| ~ spl0_20 ),
inference(backward_demodulation,[],[f148,f176]) ).
fof(f189,plain,
( 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) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_16
| ~ spl0_20 ),
inference(backward_demodulation,[],[f153,f176]) ).
fof(f190,plain,
( 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) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_17
| ~ spl0_20 ),
inference(backward_demodulation,[],[f158,f176]) ).
fof(f191,plain,
( class_Ring__and__Field_Oordered__idom(t_b) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_18
| ~ spl0_20 ),
inference(backward_demodulation,[],[f163,f176]) ).
fof(f199,definition,
( spl0_22
<=> class_Ring__and__Field_Oordered__idom(t_b) = class_Ring__and__Field_Opordered__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f201,plain,
( class_Ring__and__Field_Oordered__idom(t_b) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f202,plain,
( spl0_22
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f191,f174,f161,f199]) ).
fof(f204,definition,
( spl0_23
<=> 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) = class_Ring__and__Field_Opordered__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f206,plain,
( 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) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,plain,
( spl0_23
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f190,f174,f156,f204]) ).
fof(f209,definition,
( spl0_24
<=> 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) = class_Ring__and__Field_Opordered__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f211,plain,
( 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) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,plain,
( spl0_24
| ~ spl0_16
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f189,f174,f151,f209]) ).
fof(f214,definition,
( spl0_25
<=> 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) = class_Ring__and__Field_Opordered__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f217,plain,
( ~ spl0_25
| spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f188,f174,f146,f214]) ).
fof(f219,definition,
( spl0_26
<=> c_less(c_0,v_c,t_b) = class_Ring__and__Field_Opordered__semiring(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f221,plain,
( c_less(c_0,v_c,t_b) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f222,plain,
( spl0_26
| ~ spl0_14
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f178,f174,f127,f219]) ).
fof(f227,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),class_OrderedGroup_Olordered__ab__group__abs(t_b),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22 ),
inference(superposition,[],[f187,f201]) ).
fof(f228,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f227,f2]) ).
fof(f230,definition,
( spl0_27
<=> class_Ring__and__Field_Opordered__semiring(t_b) = class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f232,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f233,plain,
( spl0_27
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f228,f199,f174,f127,f91,f33,f230]) ).
fof(f235,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),class_Orderings_Oorder(t_b),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27 ),
inference(superposition,[],[f184,f232]) ).
fof(f236,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = class_Orderings_Oorder(t_b)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f235,f2]) ).
fof(f238,definition,
( spl0_28
<=> class_Ring__and__Field_Opordered__semiring(t_b) = class_Orderings_Oorder(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f240,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = class_Orderings_Oorder(t_b)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f241,plain,
( spl0_28
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f236,f230,f174,f127,f91,f33,f238]) ).
fof(f244,plain,
( ! [X0] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27 ),
inference(superposition,[],[f183,f232]) ).
fof(f245,plain,
( ! [X0] : class_Ring__and__Field_Opordered__semiring(t_b) = c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27 ),
inference(forward_demodulation,[],[f244,f2]) ).
fof(f248,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(class_Orderings_Oorder(t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,v_c,t_b),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_26 ),
inference(superposition,[],[f182,f221]) ).
fof(f257,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Orderings_Oorder(t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,v_c,t_b),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_26 ),
inference(forward_demodulation,[],[f248,f2]) ).
fof(f261,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,v_c,t_b),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_demodulation,[],[f257,f240]) ).
fof(f272,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = c_lessequals(c_0,v_c,t_b)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_26
| ~ spl0_28 ),
inference(forward_demodulation,[],[f261,f2]) ).
fof(f274,definition,
( spl0_31
<=> class_Ring__and__Field_Opordered__semiring(t_b) = c_lessequals(c_0,v_c,t_b) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f276,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = c_lessequals(c_0,v_c,t_b)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f277,plain,
( spl0_31
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_26
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f272,f238,f219,f174,f127,f91,f33,f274]) ).
fof(f278,plain,
( ! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = ifeq2(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b),c_HOL_Oabs(c_times(X0,X1,t_b),t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22 ),
inference(superposition,[],[f179,f201]) ).
fof(f279,plain,
( ! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f278,f1]) ).
fof(f303,plain,
( ! [X0] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(c_0,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,c_times(v_c,X0,t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_31 ),
inference(superposition,[],[f181,f276]) ).
fof(f312,plain,
( ! [X0] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(c_0,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,c_times(v_c,X0,t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_31 ),
inference(forward_demodulation,[],[f303,f2]) ).
fof(f319,plain,
( ! [X0] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(c_0,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,c_times(v_c,X0,t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_31 ),
inference(forward_demodulation,[],[f312,f176]) ).
fof(f329,plain,
( ! [X0] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,c_times(v_c,X0,t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_31 ),
inference(forward_demodulation,[],[f319,f2]) ).
fof(f390,plain,
( ! [X0,X1] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(X1,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_times(X1,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_24 ),
inference(superposition,[],[f180,f211]) ).
fof(f406,plain,
( ! [X0,X1] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(X1,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_times(X1,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_24 ),
inference(forward_demodulation,[],[f390,f2]) ).
fof(f424,plain,
( ! [X0,X1] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(X1,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_times(X1,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_24 ),
inference(forward_demodulation,[],[f406,f2]) ).
fof(f439,plain,
( ! [X0,X1] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(X1,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_times(X1,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_24
| ~ spl0_27 ),
inference(forward_demodulation,[],[f424,f245]) ).
fof(f444,plain,
( ! [X0,X1] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(c_lessequals(X1,X0,t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_times(X1,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_24
| ~ spl0_27 ),
inference(forward_demodulation,[],[f439,f2]) ).
fof(f567,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b),ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),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_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),t_b),class_Ring__and__Field_Opordered__semiring(t_b)),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_23
| ~ spl0_24
| ~ spl0_27 ),
inference(superposition,[],[f444,f206]) ).
fof(f584,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b),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_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),t_b),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_23
| ~ spl0_24
| ~ spl0_27 ),
inference(forward_demodulation,[],[f567,f2]) ).
fof(f598,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b),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_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),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_23
| ~ spl0_24
| ~ spl0_27 ),
inference(forward_demodulation,[],[f584,f45]) ).
fof(f619,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b),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),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22
| ~ spl0_23
| ~ spl0_24
| ~ spl0_27 ),
inference(forward_demodulation,[],[f598,f279]) ).
fof(f621,definition,
( spl0_42
<=> class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b),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),class_Ring__and__Field_Opordered__semiring(t_b)) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f623,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b),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),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f624,plain,
( spl0_42
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22
| ~ spl0_23
| ~ spl0_24
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f619,f230,f209,f204,f199,f174,f127,f91,f43,f33,f621]) ).
fof(f797,plain,
( ! [X0] : class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(X0,t_b),t_b),t_b),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27
| ~ spl0_31 ),
inference(superposition,[],[f329,f245]) ).
fof(f816,plain,
( ! [X0] : class_Ring__and__Field_Opordered__semiring(t_b) = c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(X0,t_b),t_b),t_b)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27
| ~ spl0_31 ),
inference(forward_demodulation,[],[f797,f2]) ).
fof(f834,plain,
( class_Ring__and__Field_Opordered__semiring(t_b) = ifeq(class_Ring__and__Field_Opordered__semiring(t_b),class_Ring__and__Field_Opordered__semiring(t_b),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),class_Ring__and__Field_Opordered__semiring(t_b))
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27
| ~ spl0_31
| ~ spl0_42 ),
inference(backward_demodulation,[],[f623,f816]) ).
fof(f844,plain,
( 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) = class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27
| ~ spl0_31
| ~ spl0_42 ),
inference(forward_demodulation,[],[f834,f2]) ).
fof(f851,plain,
( spl0_25
| ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27
| ~ spl0_31
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f844,f621,f274,f230,f174,f127,f91,f33,f214]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f41]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f46]) ).
cnf(s4,plain,
spl0_4,
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f56]) ).
cnf(s6,plain,
spl0_6,
inference(sat_conversion,[],[f61]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_7 ),
inference(sat_conversion,[],[f79]) ).
cnf(s8,plain,
( ~ spl0_1
| ~ spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f84]) ).
cnf(s9,plain,
( ~ spl0_1
| ~ spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f89]) ).
cnf(s10,plain,
( ~ spl0_1
| ~ spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f94]) ).
cnf(s11,plain,
( ~ spl0_9
| ~ spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s12,plain,
( ~ spl0_8
| ~ spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f117]) ).
cnf(s13,plain,
( spl0_7
| ~ spl0_10
| ~ spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s15,plain,
( ~ spl0_1
| ~ spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s16,plain,
( spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f149]) ).
cnf(s17,plain,
( ~ spl0_12
| ~ spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f154]) ).
cnf(s18,plain,
( ~ spl0_11
| ~ spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f159]) ).
cnf(s19,plain,
( ~ spl0_10
| ~ spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f164]) ).
cnf(s21,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f177]) ).
cnf(s23,plain,
( ~ spl0_18
| ~ spl0_20
| spl0_22 ),
inference(sat_conversion,[],[f202]) ).
cnf(s24,plain,
( ~ spl0_17
| ~ spl0_20
| spl0_23 ),
inference(sat_conversion,[],[f207]) ).
cnf(s25,plain,
( ~ spl0_16
| ~ spl0_20
| spl0_24 ),
inference(sat_conversion,[],[f212]) ).
cnf(s26,plain,
( spl0_15
| ~ spl0_20
| ~ spl0_25 ),
inference(sat_conversion,[],[f217]) ).
cnf(s27,plain,
( ~ spl0_14
| ~ spl0_20
| spl0_26 ),
inference(sat_conversion,[],[f222]) ).
cnf(s28,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22
| spl0_27 ),
inference(sat_conversion,[],[f233]) ).
cnf(s29,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f241]) ).
cnf(s32,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_26
| ~ spl0_28
| spl0_31 ),
inference(sat_conversion,[],[f277]) ).
cnf(s45,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| ~ spl0_22
| ~ spl0_23
| ~ spl0_24
| ~ spl0_27
| spl0_42 ),
inference(sat_conversion,[],[f624]) ).
cnf(s60,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_14
| ~ spl0_20
| spl0_25
| ~ spl0_27
| ~ spl0_31
| ~ spl0_42 ),
inference(sat_conversion,[],[f851]) ).
cnf(s62,plain,
spl0_10,
inference(rat,[],[s10,s6,s1]) ).
cnf(s63,plain,
spl0_9,
inference(rat,[],[s9,s5,s1]) ).
cnf(s64,plain,
spl0_8,
inference(rat,[],[s8,s4,s1]) ).
cnf(s65,plain,
~ spl0_7,
inference(rat,[],[s7,s2,s1]) ).
cnf(s66,plain,
spl0_14,
inference(rat,[],[s15,s1,s62]) ).
cnf(s67,plain,
spl0_11,
inference(rat,[],[s11,s62,s63]) ).
cnf(s68,plain,
spl0_12,
inference(rat,[],[s12,s62,s64]) ).
cnf(s69,plain,
~ spl0_13,
inference(rat,[],[s13,s62,s65]) ).
cnf(s71,plain,
spl0_18,
inference(rat,[],[s19,s62,s66]) ).
cnf(s72,plain,
spl0_17,
inference(rat,[],[s18,s66,s67]) ).
cnf(s73,plain,
spl0_16,
inference(rat,[],[s17,s66,s68]) ).
cnf(s74,plain,
~ spl0_15,
inference(rat,[],[s16,s66,s69]) ).
cnf(s75,plain,
spl0_20,
inference(rat,[],[s21,s66,s62,s1,s71]) ).
cnf(s76,plain,
spl0_26,
inference(rat,[],[s27,s66,s75]) ).
cnf(s77,plain,
~ spl0_25,
inference(rat,[],[s26,s74,s75]) ).
cnf(s78,plain,
spl0_24,
inference(rat,[],[s25,s73,s75]) ).
cnf(s79,plain,
spl0_23,
inference(rat,[],[s24,s72,s75]) ).
cnf(s80,plain,
spl0_22,
inference(rat,[],[s23,s71,s75]) ).
cnf(s83,plain,
spl0_27,
inference(rat,[],[s28,s75,s66,s62,s1,s80]) ).
cnf(s84,plain,
spl0_28,
inference(rat,[],[s29,s75,s66,s62,s1,s83]) ).
cnf(s88,plain,
spl0_42,
inference(rat,[],[s45,s80,s75,s78,s79,s66,s62,s1,s3,s83]) ).
cnf(s89,plain,
spl0_31,
inference(rat,[],[s32,s76,s75,s66,s62,s1,s84]) ).
cnf(s92,plain,
$false,
inference(rat,[],[s60,s83,s77,s75,s66,s62,s1,s88,s89]) ).
fof(f857,plain,
$false,
inference(avatar_sat_refutation,[],[s92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:32:30 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.09/1.16 % (2133485)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.09/1.16 % (2133566)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1715040004:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.09/1.16 % (2133569)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3049394897:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.09/1.16 % (2133574)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2810984164:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.09/1.16 % (2133567)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1651455461:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.09/1.16 % (2133573)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1472283058:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.09/1.16 % (2133570)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2665321084:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.09/1.16 % (2133572)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2667385011:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.09/1.16 % (2133573)First to succeed.
% 1.09/1.16 % (2133573)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2133485"
% 1.09/1.16 % (2133570)Also succeeded, but the first one will report.
% 1.09/1.16 % (2133574)Also succeeded, but the first one will report.
% 1.09/1.16 % (2133572)Also succeeded, but the first one will report.
% 1.09/1.16 % (2133573)Refutation found. Thanks to Tanya!
% 1.09/1.16 % SZS status Unsatisfiable for theBenchmark
% 1.09/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 3.98/1.35 % (2133573)------------------------------
% 3.98/1.35 % (2133573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.35 % (2133573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.35 % (2133573)CaDiCaL version: 2.1.3
% 3.98/1.35 % (2133573)Termination reason: Refutation
% 3.98/1.35 % (2133573)Time elapsed: 0.039 s
% 3.98/1.35 % (2133573)Peak memory usage: 90 MB
% 3.98/1.35 % (2133573)Instructions burned: 64 (million)
% 3.98/1.35 % (2133573)------------------------------
% 3.98/1.35 % (2133573)------------------------------
% 3.98/1.35 % (2133485)Success in time 0.484 s
% 3.98/1.35 % Vampire exiting
%------------------------------------------------------------------------------