%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA026-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 : Fri Sep 25 12:55:39 PM UTC 2026
% Result : Unsatisfiable 144.38s 25.38s
% Output : CNFRefutation 144.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 37
% Syntax : Number of formulae : 236 ( 100 unt; 7 def)
% Number of atoms : 542 ( 129 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 354 ( 174 ~; 180 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 8 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 410 ( 0 sgn 410 !; 0 ?; 337 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(v_g(X0),v_k(X0),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X2,X0,X1] :
( c_minus(X1,X2,X0) = c_plus(X1,c_uminus(X2,X0),X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0) ).
fof(f5,axiom,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f6,axiom,
! [X0,X1] :
( c_HOL_Oabs(c_uminus(X1,X0),X0) = c_HOL_Oabs(X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f7,plain,
! [X0,X1] :
( c_HOL_Oabs(X1,X0) = c_HOL_Oabs(c_uminus(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0,X1] :
( c_HOL_Oabs(X1,X0) = c_uminus(X1,X0)
| ~ c_lessequals(X1,c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_plus(X1,X2,X0),c_plus(X3,X2,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f11,axiom,
! [X0,X1] :
( c_plus(c_0,X1,X0) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f12,axiom,
! [X2,X0,X1] :
( c_minus(c_plus(X1,X2,X0),X2,X0) = X1
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__10_1) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( c_plus(X1,c_minus(X2,X3,X0),X0) = c_minus(c_plus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( c_plus(c_minus(X1,X2,X0),X3,X0) = c_minus(c_plus(X1,X3,X0),X2,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_0) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( c_minus(c_minus(X1,X2,X0),X3,X0) = c_minus(X1,c_plus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__4_0) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( c_less(X1,c_plus(X3,X2,X0),X0)
| ~ c_less(c_minus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__6_0) ).
fof(f17,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_minus(X1,X3,X0),X2,X0)
| ~ c_lessequals(X1,c_plus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
fof(f18,axiom,
! [X0,X1] :
( c_minus(X1,X1,X0) = c_0
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f19,plain,
! [X0,X1] :
( c_0 = c_minus(X1,X1,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,axiom,
! [X2,X0,X1] :
( c_uminus(c_minus(X1,X2,X0),X0) = c_minus(X2,X1,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f21,axiom,
! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_1) ).
fof(f23,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f24,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f25,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f26,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_LOrder_Ojoin__semilorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f27,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f28,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f29,axiom,
! [X0] :
( class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f30,axiom,
! [X0] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f31,axiom,
! [X0] :
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f32,axiom,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f33,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
tcf(c_80,negated_conjecture,
! [X0: $i] : c_lessequals(v_g(X0),v_k(X0),t_b),
inference(cnf_transformation,[],[f1]) ).
tcf(c_81,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[],[f2]) ).
tcf(c_82,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[],[f3]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_plus(X1,c_uminus(X2,X0),X0) = c_minus(X1,X2,X0) )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oabs(c_uminus(X1,X0),X0) = c_HOL_Oabs(X1,X0) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oabs(X0,X1) = c_uminus(X0,X1) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X0,c_0,X1) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X3,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(c_plus(X0,X1,X2),c_plus(X3,X1,X2),X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( ( c_plus(c_0,X1,X0) = X1 )
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_minus(c_plus(X1,X2,X0),X2,X0) = X1 )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_minus(c_plus(X1,X2,X0),X3,X0) = c_plus(X1,c_minus(X2,X3,X0),X0) )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_minus(c_plus(X1,X2,X0),X3,X0) = c_plus(c_minus(X1,X3,X0),X2,X0) )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_minus(c_minus(X1,X2,X0),X3,X0) = c_minus(X1,c_plus(X2,X3,X0),X0) )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_less(X0,c_plus(X3,X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_minus(X0,X1,X2),X3,X2) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_minus(X0,X2,X3),X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X0,c_plus(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( ( c_minus(X1,X1,X0) = c_0 )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_uminus(c_minus(X1,X2,X0),X0) = c_minus(X2,X1,X0) )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_less(X1,X0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Orderings_Omax(X3,X0,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X1,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X3,X0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_less(X0,X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_103,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_LOrder_Ojoin__semilorder(X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_104,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_105,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_106,plain,
! [X0: $i] :
( class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_107,plain,
! [X0: $i] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_108,plain,
! [X0: $i] :
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_109,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_110,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_429,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_plus(c_0,X2,X1) = X2 )
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_106,c_89]) ).
tcf(c_430,plain,
! [X0: $i,X1: $i] :
( ( c_plus(c_0,X1,X0) = X1 )
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_429]) ).
tcf(c_440,plain,
! [X0: $i,X1: $i] :
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_108,c_103]) ).
tcf(c_441,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_440]) ).
tcf(c_451,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_441]) ).
tcf(c_452,plain,
class_Orderings_Oorder(t_b),
inference(unflattening,[status(thm)],[c_451]) ).
tcf(c_456,plain,
! [X0: $i,X1: $i] :
( ( c_plus(c_0,X1,X0) = X1 )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_430]) ).
tcf(c_457,plain,
! [X0: $i] : c_plus(c_0,X0,t_b) = X0,
inference(unflattening,[status(thm)],[c_456]) ).
tcf(c_462,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_110]) ).
tcf(c_463,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unflattening,[status(thm)],[c_462]) ).
tcf(c_467,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__group__add(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_109]) ).
tcf(c_468,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(unflattening,[status(thm)],[c_467]) ).
tcf(c_472,plain,
! [X0: $i] :
( class_Orderings_Olinorder(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_107]) ).
tcf(c_473,plain,
class_Orderings_Olinorder(t_b),
inference(unflattening,[status(thm)],[c_472]) ).
tcf(c_482,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_102,c_452]) ).
tcf(c_483,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,t_b)
| ~ c_less(X0,X1,t_b) ),
inference(unflattening,[status(thm)],[c_482]) ).
tcf(c_491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_101,c_452]) ).
tcf(c_492,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X2,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(unflattening,[status(thm)],[c_491]) ).
tcf(c_507,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oabs(X1,X0) = c_uminus(X1,X0) )
| ~ c_lessequals(X1,c_0,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_86,c_463]) ).
tcf(c_508,plain,
! [X0: $i] :
( ( c_HOL_Oabs(X0,t_b) = c_uminus(X0,t_b) )
| ~ c_lessequals(X0,c_0,t_b) ),
inference(unflattening,[status(thm)],[c_507]) ).
tcf(c_516,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_105,c_463]) ).
tcf(c_517,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(unflattening,[status(thm)],[c_516]) ).
tcf(c_521,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_104,c_463]) ).
tcf(c_522,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unflattening,[status(thm)],[c_521]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oabs(c_uminus(X1,X0),X0) = c_HOL_Oabs(X1,X0) )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_85,c_463]) ).
tcf(c_527,plain,
! [X0: $i] : c_HOL_Oabs(c_uminus(X0,t_b),t_b) = c_HOL_Oabs(X0,t_b),
inference(unflattening,[status(thm)],[c_526]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_84,c_463]) ).
tcf(c_533,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(unflattening,[status(thm)],[c_532]) ).
tcf(c_544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_plus(X1,X2,X0),c_plus(X3,X2,X0),X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_88,c_517]) ).
tcf(c_545,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,t_b)
| ~ c_lessequals(c_plus(X0,X1,t_b),c_plus(X2,X1,t_b),t_b) ),
inference(unflattening,[status(thm)],[c_544]) ).
tcf(c_566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_less(X1,c_plus(X3,X2,X0),X0)
| ~ c_less(c_minus(X1,X2,X0),X3,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_94,c_522]) ).
tcf(c_567,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X0,c_plus(X2,X1,t_b),t_b)
| ~ c_less(c_minus(X0,X1,t_b),X2,t_b) ),
inference(unflattening,[status(thm)],[c_566]) ).
tcf(c_575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_minus(X1,X3,X0),X2,X0)
| ~ c_lessequals(X1,c_plus(X2,X3,X0),X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_95,c_522]) ).
tcf(c_576,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_minus(X0,X2,t_b),X1,t_b)
| ~ c_lessequals(X0,c_plus(X1,X2,t_b),t_b) ),
inference(unflattening,[status(thm)],[c_575]) ).
tcf(c_588,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_uminus(c_minus(X1,X2,X0),X0) = c_minus(X2,X1,X0) )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_97,c_468]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i] : c_uminus(c_minus(X0,X1,t_b),t_b) = c_minus(X1,X0,t_b),
inference(unflattening,[status(thm)],[c_588]) ).
tcf(c_594,plain,
! [X0: $i,X1: $i] :
( ( c_minus(X1,X1,X0) = c_0 )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_96,c_468]) ).
tcf(c_595,plain,
! [X0: $i] : c_minus(X0,X0,t_b) = c_0,
inference(unflattening,[status(thm)],[c_594]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_minus(c_minus(X1,X2,X0),X3,X0) = c_minus(X1,c_plus(X2,X3,X0),X0) )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_93,c_468]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(c_minus(X0,X1,t_b),X2,t_b) = c_minus(X0,c_plus(X1,X2,t_b),t_b),
inference(unflattening,[status(thm)],[c_600]) ).
tcf(c_606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_minus(c_plus(X1,X2,X0),X3,X0) = c_plus(c_minus(X1,X3,X0),X2,X0) )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_92,c_468]) ).
tcf(c_607,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(c_plus(X0,X1,t_b),X2,t_b) = c_plus(c_minus(X0,X2,t_b),X1,t_b),
inference(unflattening,[status(thm)],[c_606]) ).
tcf(c_612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_minus(c_plus(X1,X2,X0),X3,X0) = c_plus(X1,c_minus(X2,X3,X0),X0) )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_91,c_468]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(c_plus(X0,X1,t_b),X2,t_b) = c_plus(X0,c_minus(X1,X2,t_b),t_b),
inference(unflattening,[status(thm)],[c_612]) ).
tcf(c_618,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_minus(c_plus(X1,X2,X0),X2,X0) = X1 )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_468]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i] : c_minus(c_plus(X0,X1,t_b),X1,t_b) = X0,
inference(unflattening,[status(thm)],[c_618]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_plus(X1,c_uminus(X2,X0),X0) = c_minus(X1,X2,X0) )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_83,c_468]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i] : c_plus(X0,c_uminus(X1,t_b),t_b) = c_minus(X0,X1,t_b),
inference(unflattening,[status(thm)],[c_624]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_98,c_473]) ).
tcf(c_638,plain,
! [X0: $i,X1: $i] :
( c_less(X1,X0,t_b)
| c_lessequals(X0,X1,t_b) ),
inference(unflattening,[status(thm)],[c_637]) ).
tcf(c_646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,X2,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_100,c_473]) ).
tcf(c_647,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Orderings_Omax(X2,X0,t_b),X1,t_b)
| ~ c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(unflattening,[status(thm)],[c_646]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_less(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_99,c_473]) ).
tcf(c_659,plain,
! [X0: $i,X1: $i] :
( ~ c_less(X1,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(unflattening,[status(thm)],[c_658]) ).
tcf(c_674,plain,
! [X0: $i,X1: $i] :
( ~ c_lessequals(X0,X1,t_b)
| ~ c_less(X1,X0,t_b) ),
inference(prop_impl_just,[status(thm)],[c_659]) ).
tcf(c_675,plain,
! [X0: $i,X1: $i] :
( ~ c_less(X1,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(renaming,[status(thm)],[c_674]) ).
tcf(c_676,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,t_b)
| c_less(X1,X0,t_b) ),
inference(prop_impl_just,[status(thm)],[c_638]) ).
tcf(c_677,plain,
! [X0: $i,X1: $i] :
( c_less(X1,X0,t_b)
| c_lessequals(X0,X1,t_b) ),
inference(renaming,[status(thm)],[c_676]) ).
tcf(c_678,plain,
! [X0: $i,X1: $i] :
( ~ c_less(X1,X0,t_b)
| ~ c_less(X0,X1,t_b) ),
inference(prop_impl_just,[status(thm)],[c_483,c_659]) ).
tcf(c_680,plain,
! [X0: $i] :
( ( c_HOL_Oabs(X0,t_b) = c_uminus(X0,t_b) )
| ~ c_lessequals(X0,c_0,t_b) ),
inference(prop_impl_just,[status(thm)],[c_508]) ).
tcf(c_684,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,t_b)
| ~ c_lessequals(c_plus(X0,X1,t_b),c_plus(X2,X1,t_b),t_b) ),
inference(prop_impl_just,[status(thm)],[c_545]) ).
tcf(c_690,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X0,c_plus(X2,X1,t_b),t_b)
| ~ c_less(c_minus(X0,X1,t_b),X2,t_b) ),
inference(prop_impl_just,[status(thm)],[c_567]) ).
tcf(c_694,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_minus(X0,X2,t_b),X1,t_b)
| ~ c_lessequals(X0,c_plus(X1,X2,t_b),t_b) ),
inference(prop_impl_just,[status(thm)],[c_576]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X2,X1,t_b)
| c_lessequals(X0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(bin_hyper_res,[status(thm)],[c_492,c_677]) ).
tcf(c_736,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X1,X2,t_b)
| c_lessequals(c_Orderings_Omax(X0,X2,t_b),X1,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(bin_hyper_res,[status(thm)],[c_647,c_677]) ).
tcf(c_863,definition,
iPr_def_10 = v_f(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_864,definition,
iPr_def_11 = v_k(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_865,definition,
iPr_def_12 = c_minus(iPr_def_10,iPr_def_11,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_866,definition,
iPr_def_13 = c_Orderings_Omax(iPr_def_12,c_0,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_867,definition,
iPr_def_14 = v_g(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_868,definition,
iPr_def_15 = c_minus(iPr_def_10,iPr_def_14,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_869,definition,
iPr_def_16 = c_HOL_Oabs(iPr_def_15,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_870,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X1,X2,t_b)
| c_lessequals(c_Orderings_Omax(X0,X2,t_b),X1,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(demodulation,[status(thm)],[c_736]) ).
tcf(c_871,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X2,X1,t_b)
| c_lessequals(X0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(demodulation,[status(thm)],[c_735]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i] : c_plus(X0,c_uminus(X1,t_b),t_b) = c_minus(X0,X1,t_b),
inference(demodulation,[status(thm)],[c_625]) ).
tcf(c_873,plain,
! [X0: $i,X1: $i] : c_minus(c_plus(X0,X1,t_b),X1,t_b) = X0,
inference(demodulation,[status(thm)],[c_619]) ).
tcf(c_874,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(c_plus(X0,X1,t_b),X2,t_b) = c_plus(X0,c_minus(X1,X2,t_b),t_b),
inference(demodulation,[status(thm)],[c_613]) ).
tcf(c_875,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(c_plus(X0,X1,t_b),X2,t_b) = c_plus(c_minus(X0,X2,t_b),X1,t_b),
inference(demodulation,[status(thm)],[c_607]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(c_minus(X0,X1,t_b),X2,t_b) = c_minus(X0,c_plus(X1,X2,t_b),t_b),
inference(demodulation,[status(thm)],[c_601]) ).
tcf(c_877,plain,
! [X0: $i] : c_minus(X0,X0,t_b) = c_0,
inference(demodulation,[status(thm)],[c_595]) ).
tcf(c_878,plain,
! [X0: $i,X1: $i] : c_uminus(c_minus(X0,X1,t_b),t_b) = c_minus(X1,X0,t_b),
inference(demodulation,[status(thm)],[c_589]) ).
tcf(c_879,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(demodulation,[status(thm)],[c_533]) ).
tcf(c_880,plain,
! [X0: $i] : c_HOL_Oabs(c_uminus(X0,t_b),t_b) = c_HOL_Oabs(X0,t_b),
inference(demodulation,[status(thm)],[c_527]) ).
tcf(c_881,plain,
! [X0: $i] : c_plus(c_0,X0,t_b) = X0,
inference(demodulation,[status(thm)],[c_457]) ).
tcf(c_882,negated_conjecture,
~ c_lessequals(iPr_def_13,iPr_def_16,t_b),
inference(demodulation,[status(thm)],[c_81,c_867,c_868,c_869,c_864,c_863,c_865,c_866]) ).
tcf(c_883,negated_conjecture,
! [X0: $i] : c_lessequals(v_g(X0),v_k(X0),t_b),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_1435,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,t_b)
| ~ c_lessequals(c_plus(X0,c_uminus(X1,t_b),t_b),c_minus(X2,X1,t_b),t_b) ),
inference(superposition,[status(thm)],[c_872,c_684]) ).
tcf(c_1440,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,t_b)
| ~ c_lessequals(c_minus(X0,X1,t_b),c_minus(X2,X1,t_b),t_b) ),
inference(light_normalisation,[status(thm)],[c_1435,c_872]) ).
tcf(c_1449,plain,
c_lessequals(v_g(v_x),iPr_def_11,t_b),
inference(superposition,[status(thm)],[c_864,c_883]) ).
tcf(c_1450,plain,
c_lessequals(iPr_def_14,iPr_def_11,t_b),
inference(light_normalisation,[status(thm)],[c_1449,c_867]) ).
tcf(c_1453,plain,
c_lessequals(c_0,iPr_def_16,t_b),
inference(superposition,[status(thm)],[c_869,c_879]) ).
tcf(c_1497,plain,
! [X0: $i] :
( c_less(X0,iPr_def_11,t_b)
| c_lessequals(iPr_def_14,X0,t_b) ),
inference(superposition,[status(thm)],[c_1450,c_871]) ).
tcf(c_1498,plain,
! [X0: $i] :
( c_less(X0,iPr_def_16,t_b)
| c_lessequals(c_0,X0,t_b) ),
inference(superposition,[status(thm)],[c_1453,c_871]) ).
tcf(c_1529,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_minus(X0,X1,t_b),c_0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(superposition,[status(thm)],[c_881,c_694]) ).
tcf(c_1537,plain,
c_minus(iPr_def_14,iPr_def_10,t_b) = c_uminus(iPr_def_15,t_b),
inference(superposition,[status(thm)],[c_868,c_878]) ).
tcf(c_1564,plain,
! [X0: $i] :
( c_less(iPr_def_10,c_plus(X0,iPr_def_11,t_b),t_b)
| ~ c_less(iPr_def_12,X0,t_b) ),
inference(superposition,[status(thm)],[c_865,c_690]) ).
tcf(c_1594,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,t_b)
| ~ c_less(X0,X1,t_b) ),
inference(superposition,[status(thm)],[c_677,c_678]) ).
tcf(c_1795,plain,
! [X0: $i] :
( c_less(X0,c_0,t_b)
| c_lessequals(iPr_def_13,X0,t_b)
| ~ c_lessequals(iPr_def_12,X0,t_b) ),
inference(superposition,[status(thm)],[c_866,c_870]) ).
tcf(c_1901,plain,
( c_lessequals(c_uminus(iPr_def_15,t_b),c_0,t_b)
| ~ c_lessequals(iPr_def_14,iPr_def_10,t_b) ),
inference(superposition,[status(thm)],[c_1537,c_1529]) ).
tcf(c_2342,plain,
! [X0: $i] :
( c_lessequals(X0,iPr_def_10,t_b)
| ~ c_lessequals(c_minus(X0,iPr_def_11,t_b),iPr_def_12,t_b) ),
inference(superposition,[status(thm)],[c_865,c_1440]) ).
tcf(c_2469,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X0,t_b)
| c_lessequals(X0,X1,t_b) ),
inference(superposition,[status(thm)],[c_677,c_1594]) ).
tcf(c_2472,plain,
! [X0: $i] :
( c_lessequals(c_0,X0,t_b)
| c_lessequals(X0,iPr_def_16,t_b) ),
inference(superposition,[status(thm)],[c_1498,c_1594]) ).
tcf(c_2546,plain,
! [X0: $i] : c_lessequals(X0,X0,t_b),
inference(equality_factoring,[status(thm)],[c_2469]) ).
tcf(c_3025,plain,
~ c_less(iPr_def_16,c_0,t_b),
inference(superposition,[status(thm)],[c_1453,c_675]) ).
tcf(c_4249,plain,
( c_less(iPr_def_10,iPr_def_11,t_b)
| ~ c_less(iPr_def_12,c_0,t_b) ),
inference(superposition,[status(thm)],[c_881,c_1564]) ).
tcf(c_5500,plain,
( c_lessequals(iPr_def_11,iPr_def_10,t_b)
| ~ c_lessequals(c_0,iPr_def_12,t_b) ),
inference(superposition,[status(thm)],[c_877,c_2342]) ).
tcf(c_5683,plain,
( c_lessequals(iPr_def_12,iPr_def_16,t_b)
| c_lessequals(iPr_def_11,iPr_def_10,t_b) ),
inference(superposition,[status(thm)],[c_2472,c_5500]) ).
tcf(c_6392,plain,
( c_less(iPr_def_12,c_0,t_b)
| c_lessequals(iPr_def_13,iPr_def_12,t_b) ),
inference(superposition,[status(thm)],[c_2546,c_1795]) ).
tcf(c_6401,plain,
( c_less(iPr_def_16,c_0,t_b)
| c_lessequals(iPr_def_13,iPr_def_16,t_b)
| c_lessequals(iPr_def_11,iPr_def_10,t_b) ),
inference(superposition,[status(thm)],[c_5683,c_1795]) ).
tcf(c_6404,plain,
c_lessequals(iPr_def_11,iPr_def_10,t_b),
inference(forward_subsumption_resolution,[status(thm)],[c_6401,c_3025,c_882]) ).
tcf(c_6592,plain,
~ c_less(iPr_def_10,iPr_def_11,t_b),
inference(superposition,[status(thm)],[c_6404,c_675]) ).
tcf(c_6596,plain,
~ c_less(iPr_def_12,c_0,t_b),
inference(backward_subsumption_resolution,[status(thm)],[c_4249,c_6592]) ).
tcf(c_6604,plain,
c_lessequals(iPr_def_14,iPr_def_10,t_b),
inference(superposition,[status(thm)],[c_1497,c_6592]) ).
tcf(c_8524,plain,
c_lessequals(iPr_def_13,iPr_def_12,t_b),
inference(global_subsumption_just,[status(thm)],[c_6392,c_6392,c_6596]) ).
tcf(c_8527,plain,
! [X0: $i] :
( c_less(X0,iPr_def_12,t_b)
| c_lessequals(iPr_def_13,X0,t_b) ),
inference(superposition,[status(thm)],[c_8524,c_871]) ).
tcf(c_14539,plain,
! [X0: $i] : c_minus(c_0,X0,t_b) = c_uminus(X0,t_b),
inference(superposition,[status(thm)],[c_881,c_872]) ).
tcf(c_14541,plain,
! [X0: $i,X1: $i] : c_minus(c_minus(X0,X1,t_b),c_uminus(X1,t_b),t_b) = X0,
inference(superposition,[status(thm)],[c_872,c_873]) ).
tcf(c_14551,plain,
! [X0: $i] : c_minus(X0,c_0,t_b) = X0,
inference(demodulation,[status(thm)],[c_14541,c_877,c_876,c_872]) ).
tcf(c_14561,plain,
! [X0: $i] : c_uminus(c_uminus(X0,t_b),t_b) = c_minus(X0,c_0,t_b),
inference(superposition,[status(thm)],[c_14539,c_878]) ).
tcf(c_14563,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(X0,c_minus(X1,X2,t_b),t_b) = c_plus(X0,c_minus(X2,X1,t_b),t_b),
inference(superposition,[status(thm)],[c_878,c_872]) ).
tcf(c_14565,plain,
! [X0: $i] : c_uminus(c_uminus(X0,t_b),t_b) = X0,
inference(light_normalisation,[status(thm)],[c_14561,c_14551]) ).
tcf(c_14607,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(c_plus(X0,X1,t_b),X2,t_b) = c_minus(X0,c_minus(X2,X1,t_b),t_b),
inference(demodulation,[status(thm)],[c_874,c_14563]) ).
tcf(c_14629,plain,
c_minus(iPr_def_14,iPr_def_10,t_b) = c_uminus(iPr_def_15,t_b),
inference(superposition,[status(thm)],[c_868,c_878]) ).
tcf(c_14742,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(X0,c_minus(X1,X2,t_b),t_b) = c_plus(c_minus(X0,X1,t_b),X2,t_b),
inference(light_normalisation,[status(thm)],[c_875,c_14607]) ).
tcf(c_14745,plain,
! [X0: $i,X1: $i] : c_minus(X0,c_minus(X0,X1,t_b),t_b) = c_plus(c_0,X1,t_b),
inference(superposition,[status(thm)],[c_877,c_14742]) ).
tcf(c_14764,plain,
! [X0: $i,X1: $i] : c_minus(X0,c_plus(X0,X1,t_b),t_b) = c_minus(c_0,X1,t_b),
inference(superposition,[status(thm)],[c_877,c_876]) ).
tcf(c_14953,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_minus(X0,X1,t_b),c_0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(superposition,[status(thm)],[c_881,c_694]) ).
tcf(c_15241,plain,
( c_lessequals(c_uminus(iPr_def_15,t_b),c_0,t_b)
| ~ c_lessequals(iPr_def_14,iPr_def_10,t_b) ),
inference(superposition,[status(thm)],[c_14629,c_14953]) ).
tcf(c_16933,plain,
c_lessequals(c_uminus(iPr_def_15,t_b),c_0,t_b),
inference(global_subsumption_just,[status(thm)],[c_15241,c_1901,c_6604]) ).
tcf(c_16937,plain,
c_HOL_Oabs(c_uminus(iPr_def_15,t_b),t_b) = c_uminus(c_uminus(iPr_def_15,t_b),t_b),
inference(superposition,[status(thm)],[c_16933,c_680]) ).
tcf(c_29648,plain,
iPr_def_15 = iPr_def_16,
inference(demodulation,[status(thm)],[c_16937,c_880,c_869,c_14565]) ).
tcf(c_33469,plain,
! [X0: $i,X1: $i] : c_minus(X0,c_minus(X0,X1,t_b),t_b) = X1,
inference(demodulation,[status(thm)],[c_14745,c_881]) ).
tcf(c_36255,plain,
! [X0: $i,X1: $i] : c_minus(X0,c_plus(X0,X1,t_b),t_b) = c_uminus(X1,t_b),
inference(demodulation,[status(thm)],[c_14764,c_14539]) ).
tcf(c_36264,plain,
! [X0: $i,X1: $i] : c_minus(X0,c_uminus(X1,t_b),t_b) = c_plus(X0,X1,t_b),
inference(superposition,[status(thm)],[c_36255,c_33469]) ).
tcf(c_204508,plain,
! [X0: $i] : c_minus(c_0,X0,t_b) = c_uminus(X0,t_b),
inference(superposition,[status(thm)],[c_872,c_881]) ).
tcf(c_204516,plain,
! [X0: $i,X1: $i] : c_minus(X0,c_plus(X1,X0,t_b),t_b) = c_uminus(X1,t_b),
inference(superposition,[status(thm)],[c_873,c_878]) ).
tcf(c_204517,plain,
! [X0: $i] : c_uminus(c_uminus(X0,t_b),t_b) = c_minus(X0,c_0,t_b),
inference(superposition,[status(thm)],[c_204508,c_878]) ).
tcf(c_204519,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(X0,c_minus(X1,X2,t_b),t_b) = c_plus(X0,c_minus(X2,X1,t_b),t_b),
inference(superposition,[status(thm)],[c_878,c_872]) ).
tcf(c_204523,plain,
! [X0: $i] : c_minus(X0,c_0,t_b) = X0,
inference(light_normalisation,[status(thm)],[c_204517,c_14565]) ).
tcf(c_204707,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(c_plus(X0,X1,t_b),X2,t_b) = c_minus(X0,c_minus(X2,X1,t_b),t_b),
inference(demodulation,[status(thm)],[c_874,c_204519]) ).
tcf(c_205174,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(X0,c_minus(X1,X2,t_b),t_b) = c_plus(c_minus(X0,X1,t_b),X2,t_b),
inference(light_normalisation,[status(thm)],[c_875,c_204707]) ).
tcf(c_205177,plain,
! [X0: $i,X1: $i] : c_minus(X0,c_minus(X0,X1,t_b),t_b) = c_plus(c_0,X1,t_b),
inference(superposition,[status(thm)],[c_877,c_205174]) ).
tcf(c_215965,plain,
! [X0: $i,X1: $i] : c_minus(X0,c_minus(X0,X1,t_b),t_b) = X1,
inference(demodulation,[status(thm)],[c_205177,c_881]) ).
tcf(c_215976,plain,
! [X0: $i,X1: $i] : c_minus(X0,c_uminus(X1,t_b),t_b) = c_plus(X1,X0,t_b),
inference(superposition,[status(thm)],[c_204516,c_215965]) ).
tcf(c_354415,plain,
! [X0: $i] :
( ~ c_less(X0,iPr_def_12,t_b)
| ~ c_lessequals(iPr_def_12,X0,t_b) ),
inference(instantiation,[status(thm)],[c_675]) ).
tcf(c_422669,plain,
~ c_lessequals(iPr_def_13,iPr_def_15,t_b),
inference(light_normalisation,[status(thm)],[c_882,c_29648]) ).
tcf(c_422677,plain,
c_lessequals(v_g(v_x),iPr_def_11,t_b),
inference(superposition,[status(thm)],[c_864,c_883]) ).
tcf(c_422678,plain,
c_lessequals(iPr_def_14,iPr_def_11,t_b),
inference(light_normalisation,[status(thm)],[c_422677,c_867]) ).
tcf(c_422701,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(X0,c_minus(X1,X2,t_b),t_b) = c_plus(X0,c_minus(X2,X1,t_b),t_b),
inference(superposition,[status(thm)],[c_878,c_872]) ).
tcf(c_422749,plain,
! [X0: $i] :
( c_less(X0,c_0,t_b)
| c_lessequals(iPr_def_13,X0,t_b)
| ~ c_lessequals(iPr_def_12,X0,t_b) ),
inference(superposition,[status(thm)],[c_866,c_870]) ).
tcf(c_422859,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(c_plus(X0,X1,t_b),X2,t_b) = c_minus(X0,c_minus(X2,X1,t_b),t_b),
inference(demodulation,[status(thm)],[c_874,c_422701]) ).
tcf(c_422895,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,t_b)
| ~ c_lessequals(c_plus(X0,c_uminus(X1,t_b),t_b),c_minus(X2,X1,t_b),t_b) ),
inference(superposition,[status(thm)],[c_872,c_684]) ).
tcf(c_422903,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,t_b)
| ~ c_lessequals(c_minus(X0,X1,t_b),c_minus(X2,X1,t_b),t_b) ),
inference(light_normalisation,[status(thm)],[c_422895,c_872]) ).
tcf(c_422952,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_minus(X0,X1,t_b),c_0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(superposition,[status(thm)],[c_881,c_694]) ).
tcf(c_423092,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(X0,c_minus(X1,X2,t_b),t_b) = c_plus(c_minus(X0,X1,t_b),X2,t_b),
inference(light_normalisation,[status(thm)],[c_875,c_422859]) ).
tcf(c_423096,plain,
! [X0: $i] : c_minus(iPr_def_10,c_minus(iPr_def_11,X0,t_b),t_b) = c_plus(iPr_def_12,X0,t_b),
inference(superposition,[status(thm)],[c_865,c_423092]) ).
tcf(c_423136,plain,
! [X0: $i,X1: $i,X2: $i] : c_uminus(c_minus(X0,c_plus(X1,X2,t_b),t_b),t_b) = c_minus(X2,c_minus(X0,X1,t_b),t_b),
inference(superposition,[status(thm)],[c_876,c_878]) ).
tcf(c_423236,plain,
! [X0: $i,X1: $i,X2: $i] : c_minus(X0,c_minus(X1,X2,t_b),t_b) = c_minus(X2,c_minus(X1,X0,t_b),t_b),
inference(demodulation,[status(thm)],[c_423136,c_878,c_422859]) ).
tcf(c_423261,plain,
! [X0: $i] : c_minus(iPr_def_14,c_minus(iPr_def_10,X0,t_b),t_b) = c_minus(X0,iPr_def_15,t_b),
inference(superposition,[status(thm)],[c_868,c_423236]) ).
tcf(c_424679,plain,
! [X0: $i] :
( ~ c_lessequals(iPr_def_12,X0,t_b)
| c_lessequals(iPr_def_13,X0,t_b) ),
inference(global_subsumption_just,[status(thm)],[c_422749,c_8527,c_354415]) ).
tcf(c_424680,plain,
! [X0: $i] :
( c_lessequals(iPr_def_13,X0,t_b)
| ~ c_lessequals(iPr_def_12,X0,t_b) ),
inference(renaming,[status(thm)],[c_424679]) ).
tcf(c_424891,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,t_b)
| ~ c_lessequals(c_minus(X0,X1,t_b),c_0,t_b) ),
inference(superposition,[status(thm)],[c_877,c_422903]) ).
tcf(c_427434,plain,
! [X0: $i,X1: $i] : c_plus(X0,X1,t_b) = c_plus(X1,X0,t_b),
inference(superposition,[status(thm)],[c_36264,c_215976]) ).
tcf(c_429329,plain,
c_minus(iPr_def_10,c_0,t_b) = c_plus(iPr_def_12,iPr_def_11,t_b),
inference(superposition,[status(thm)],[c_877,c_423096]) ).
tcf(c_429439,plain,
c_plus(iPr_def_11,iPr_def_12,t_b) = iPr_def_10,
inference(demodulation,[status(thm)],[c_429329,c_204523,c_427434]) ).
tcf(c_429449,plain,
! [X0: $i] : c_minus(iPr_def_11,c_minus(X0,iPr_def_12,t_b),t_b) = c_minus(iPr_def_10,X0,t_b),
inference(superposition,[status(thm)],[c_429439,c_422859]) ).
tcf(c_429565,plain,
c_minus(iPr_def_10,iPr_def_12,t_b) = c_minus(iPr_def_11,c_0,t_b),
inference(superposition,[status(thm)],[c_877,c_429449]) ).
tcf(c_430149,plain,
c_minus(iPr_def_10,iPr_def_12,t_b) = iPr_def_11,
inference(demodulation,[status(thm)],[c_429565,c_204523]) ).
tcf(c_433544,plain,
c_minus(iPr_def_12,iPr_def_15,t_b) = c_minus(iPr_def_14,iPr_def_11,t_b),
inference(superposition,[status(thm)],[c_430149,c_423261]) ).
tcf(c_433648,plain,
( c_lessequals(c_minus(iPr_def_12,iPr_def_15,t_b),c_0,t_b)
| ~ c_lessequals(iPr_def_14,iPr_def_11,t_b) ),
inference(superposition,[status(thm)],[c_433544,c_422952]) ).
tcf(c_433661,plain,
c_lessequals(c_minus(iPr_def_12,iPr_def_15,t_b),c_0,t_b),
inference(forward_subsumption_resolution,[status(thm)],[c_433648,c_422678]) ).
tcf(c_433781,plain,
c_lessequals(iPr_def_12,iPr_def_15,t_b),
inference(superposition,[status(thm)],[c_433661,c_424891]) ).
tcf(c_433787,plain,
c_lessequals(iPr_def_13,iPr_def_15,t_b),
inference(superposition,[status(thm)],[c_433781,c_424680]) ).
tcf(c_433788,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_433787,c_422669]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA026-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 05:52:28 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 144.38/25.38 % SZS status Started for theBenchmark.p
% 144.38/25.38 % SZS status Unsatisfiable for theBenchmark.p
% 144.38/25.38
% 144.38/25.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 144.38/25.38
% 144.38/25.38 % ------ iProver source info
% 144.38/25.38
% 144.38/25.38 % git: date: 2026-07-19 20:42:38 +0200
% 144.38/25.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 144.38/25.38 % git: non_committed_changes: false
% 144.38/25.38
% 144.38/25.38 % ------ Parsing...% successful
% 144.38/25.38
% 144.38/25.38
% 144.38/25.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 144.38/25.38
% 144.38/25.38 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 144.38/25.38
% 144.38/25.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 144.38/25.38
% 144.38/25.38 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 144.38/25.38 % ------ Proving...
% 144.38/25.38 % ------ Problem Properties
% 144.38/25.38
% 144.38/25.38 %
% 144.38/25.38 % clauses 29
% 144.38/25.38 % conjectures 2
% 144.38/25.38 % EPR 5
% 144.38/25.38 % Horn 25
% 144.38/25.38 % unary 19
% 144.38/25.38 % binary 8
% 144.38/25.38 % lits 41
% 144.38/25.38 % lits eq 17
% 144.38/25.38 % fd_pure 0
% 144.38/25.38 % fd_pseudo 0
% 144.38/25.38 % fd_cond 0
% 144.38/25.38 % fd_pseudo_cond 0
% 144.38/25.38 % AC symbols 0
% 144.38/25.38
% 144.38/25.38 % ------ Schedule dynamic 5 is on
% 144.38/25.38
% 144.38/25.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 144.38/25.38
% 144.38/25.38
% 144.38/25.38 % ------
% 144.38/25.38 % Current options:
% 144.38/25.38 % ------
% 144.38/25.38
% 144.38/25.38
% 144.38/25.38 %
% 144.38/25.38
% 144.38/25.38 % ------ Proving...
% 144.38/25.38 % Proof_search_loop: time out after: 5067 full_loop iterations
% 144.38/25.38
% 144.38/25.38 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 144.38/25.38
% 144.38/25.38
% 144.38/25.38 % ------
% 144.38/25.38 % Current options:
% 144.38/25.38 % ------
% 144.38/25.38
% 144.38/25.38
% 144.38/25.38 %
% 144.38/25.38
% 144.38/25.38 % ------ Proving...
% 144.38/25.38 %
% 144.38/25.38
% 144.38/25.38 % SZS status Unsatisfiable for theBenchmark.p
% 144.38/25.38
% 144.38/25.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 144.38/25.39
% 144.38/25.39
%------------------------------------------------------------------------------