%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA009-1 : 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 : n012.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 12:55:35 PM UTC 2026
% Result : Unsatisfiable 65.02s 9.60s
% Output : CNFRefutation 65.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 98 ( 34 unt; 5 def)
% Number of atoms : 210 ( 29 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 165 ( 85 ~; 80 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 16 ( 14 usr; 6 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 121 ( 0 sgn 121 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
fof(f963,axiom,
! [X0] :
( c_NatArith_Oof__nat(c_0,X0) = c_0
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_NatArith_Oof__nat__eq__0__iff_1) ).
fof(f964,plain,
! [X0] :
( c_0 = c_NatArith_Oof__nat(c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(reorient_equations,[],[f963]) ).
fof(f1456,axiom,
! [X2,X0,X1] :
( c_less(X1,X2,X0)
| ~ c_less(c_minus(X1,X2,X0),c_0,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f1458,axiom,
! [X2,X0,X1] :
( c_minus(X1,c_uminus(X2,X0),X0) = c_plus(X1,X2,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f1459,plain,
! [X2,X0,X1] :
( c_plus(X1,X2,X0) = c_minus(X1,c_uminus(X2,X0),X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(reorient_equations,[],[f1458]) ).
fof(f1477,axiom,
! [X0,X1] :
( c_uminus(c_uminus(X1,X0),X0) = X1
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Ominus__minus_0) ).
fof(f1887,axiom,
! [X0,X1] :
( c_uminus(c_SetInterval_OatLeast(X1,X0),tc_set(X0)) = c_SetInterval_OlessThan(X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OCompl__atLeast_0) ).
fof(f1909,axiom,
! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| ~ c_in(X1,c_SetInterval_OatLeast(X2,X0),X0)
| ~ class_Orderings_Oord(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OatLeast__iff_0) ).
fof(f1910,axiom,
! [X2,X0,X1] :
( c_in(X2,c_SetInterval_OatLeast(X1,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oord(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OatLeast__iff_1) ).
fof(f1955,axiom,
! [X2,X0,X1] :
( c_less(X1,X2,X0)
| ~ c_in(X1,c_SetInterval_OlessThan(X2,X0),X0)
| ~ class_Orderings_Oord(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OlessThan__iff_0) ).
fof(f1956,axiom,
! [X2,X0,X1] :
( c_in(X1,c_SetInterval_OlessThan(X2,X0),X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oord(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_SetInterval_OlessThan__iff_1) ).
fof(f1973,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Set_OCompl__iff_0) ).
fof(f1974,axiom,
! [X2,X0,X1] :
( c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-1.ax',cls_Set_OCompl__iff_1) ).
fof(f3025,axiom,
! [X0] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f3032,axiom,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f3038,axiom,
! [X0] :
( class_Orderings_Oord(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f3048,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f3049,axiom,
! [X0] :
( class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f3364,negated_conjecture,
! [X0] : c_lessequals(v_lb(X0),v_f(X0),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3366,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3367,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tcf(c_3538,plain,
! [X0: $i] :
( ( c_NatArith_Oof__nat(c_0,X0) = c_0 )
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[],[f964]) ).
tcf(c_3850,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_minus(X0,X1,X2),c_0,X2) ),
inference(cnf_transformation,[],[f1456]) ).
tcf(c_3852,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_minus(X1,c_uminus(X2,X0),X0) = c_plus(X1,X2,X0) )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f1459]) ).
tcf(c_3864,plain,
! [X0: $i,X1: $i] :
( ( c_uminus(c_uminus(X1,X0),X0) = X1 )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f1477]) ).
tcf(c_4060,plain,
! [X0: $i,X1: $i] :
( ( c_uminus(c_SetInterval_OatLeast(X1,X0),tc_set(X0)) = c_SetInterval_OlessThan(X1,X0) )
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f1887]) ).
tcf(c_4076,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,X0,X2)
| ~ class_Orderings_Oord(X2)
| ~ c_in(X0,c_SetInterval_OatLeast(X1,X2),X2) ),
inference(cnf_transformation,[],[f1909]) ).
tcf(c_4077,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,c_SetInterval_OatLeast(X0,X2),X2)
| ~ class_Orderings_Oord(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f1910]) ).
tcf(c_4114,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X0,X1,X2)
| ~ class_Orderings_Oord(X2)
| ~ c_in(X0,c_SetInterval_OlessThan(X1,X2),X2) ),
inference(cnf_transformation,[],[f1955]) ).
tcf(c_4115,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,c_SetInterval_OlessThan(X1,X2),X2)
| ~ class_Orderings_Oord(X2)
| ~ c_less(X0,X1,X2) ),
inference(cnf_transformation,[],[f1956]) ).
tcf(c_4127,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_in(X0,X1,X2)
| ~ c_in(X0,c_uminus(X1,tc_set(X2)),X2) ),
inference(cnf_transformation,[],[f1973]) ).
tcf(c_4128,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,X1,X2)
| c_in(X0,c_uminus(X1,tc_set(X2)),X2) ),
inference(cnf_transformation,[],[f1974]) ).
tcf(c_4988,plain,
! [X0: $i] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3025]) ).
tcf(c_4995,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3032]) ).
tcf(c_5001,plain,
! [X0: $i] :
( class_Orderings_Oord(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3038]) ).
tcf(c_5011,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3048]) ).
tcf(c_5012,plain,
! [X0: $i] :
( class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3049]) ).
tcf(c_5302,negated_conjecture,
! [X0: $i] : c_lessequals(v_lb(X0),v_f(X0),t_b),
inference(cnf_transformation,[],[f3364]) ).
tcf(c_5304,negated_conjecture,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[],[f3366]) ).
tcf(c_5305,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[],[f3367]) ).
tcf(c_7957,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Oab__group__add(X0) ),
inference(prop_impl_just,[status(thm)],[c_4995]) ).
tcf(c_7958,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(renaming,[status(thm)],[c_7957]) ).
tcf(c_8581,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(prop_impl_just,[status(thm)],[c_5011]) ).
tcf(c_8582,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(renaming,[status(thm)],[c_8581]) ).
tcf(c_8829,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Orderings_Olinorder(X0) ),
inference(prop_impl_just,[status(thm)],[c_4988]) ).
tcf(c_8830,plain,
! [X0: $i] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(renaming,[status(thm)],[c_8829]) ).
tcf(c_9477,plain,
! [X0: $i] :
( class_Orderings_Oord(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(prop_impl_just,[status(thm)],[c_5001]) ).
tcf(c_9583,plain,
! [X0: $i] :
( class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(prop_impl_just,[status(thm)],[c_5012]) ).
tcf(c_9755,plain,
! [X0: $i] :
( ( c_NatArith_Oof__nat(c_0,X0) = c_0 )
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(prop_impl_just,[status(thm)],[c_3538]) ).
tcf(c_53809,plain,
! [X0: $i] :
( class_Ring__and__Field_Oordered__semidom(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_5305,c_9583]) ).
tcf(c_53810,plain,
class_Ring__and__Field_Oordered__semidom(t_b),
inference(unflattening,[status(thm)],[c_53809]) ).
tcf(c_53814,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_5305,c_8582]) ).
tcf(c_53815,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unflattening,[status(thm)],[c_53814]) ).
tcf(c_53834,plain,
! [X0: $i] :
( class_Orderings_Oord(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_5305,c_9477]) ).
tcf(c_53835,plain,
class_Orderings_Oord(t_b),
inference(unflattening,[status(thm)],[c_53834]) ).
tcf(c_53844,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__group__add(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_5305,c_7958]) ).
tcf(c_53845,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(unflattening,[status(thm)],[c_53844]) ).
tcf(c_53864,plain,
! [X0: $i] :
( class_Orderings_Olinorder(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_5305,c_8830]) ).
tcf(c_53865,plain,
class_Orderings_Olinorder(t_b),
inference(unflattening,[status(thm)],[c_53864]) ).
tcf(c_56805,plain,
! [X0: $i] :
( ( c_NatArith_Oof__nat(c_0,X0) = c_0 )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_9755,c_53810]) ).
tcf(c_56806,plain,
c_NatArith_Oof__nat(c_0,t_b) = c_0,
inference(unflattening,[status(thm)],[c_56805]) ).
tcf(c_135414,definition,
iPr_def_10 = c_NatArith_Oof__nat(c_0,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_135418,definition,
iPr_def_14 = v_f(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_135419,definition,
iPr_def_15 = v_lb(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_135420,definition,
iPr_def_16 = c_uminus(iPr_def_15,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_135421,definition,
iPr_def_17 = c_plus(iPr_def_14,iPr_def_16,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_135424,plain,
iPr_def_10 = c_0,
inference(demodulation,[status(thm)],[c_56806,c_135414]) ).
tcf(c_135454,plain,
class_Orderings_Olinorder(t_b),
inference(demodulation,[status(thm)],[c_53865]) ).
tcf(c_135458,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(demodulation,[status(thm)],[c_53845]) ).
tcf(c_135460,plain,
class_Orderings_Oord(t_b),
inference(demodulation,[status(thm)],[c_53835]) ).
tcf(c_135464,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(demodulation,[status(thm)],[c_53815]) ).
tcf(c_135475,negated_conjecture,
~ c_lessequals(c_0,iPr_def_17,t_b),
inference(demodulation,[status(thm)],[c_5304,c_135419,c_135420,c_135418,c_135421]) ).
tcf(c_135477,negated_conjecture,
! [X0: $i] : c_lessequals(v_lb(X0),v_f(X0),t_b),
inference(demodulation,[status(thm)],[c_5302]) ).
tcf(c_161125,plain,
~ c_lessequals(iPr_def_10,iPr_def_17,t_b),
inference(light_normalisation,[status(thm)],[c_135475,c_135424]) ).
tcf(c_162139,plain,
c_lessequals(v_lb(v_x),iPr_def_14,t_b),
inference(superposition,[status(thm)],[c_135418,c_135477]) ).
tcf(c_162140,plain,
c_lessequals(iPr_def_15,iPr_def_14,t_b),
inference(light_normalisation,[status(thm)],[c_162139,c_135419]) ).
tcf(c_168024,plain,
! [X0: $i] : c_uminus(c_uminus(X0,t_b),t_b) = X0,
inference(superposition,[status(thm)],[c_135458,c_3864]) ).
tcf(c_168181,plain,
c_uminus(iPr_def_16,t_b) = iPr_def_15,
inference(superposition,[status(thm)],[c_135420,c_168024]) ).
tcf(c_198588,plain,
! [X0: $i] : c_uminus(c_SetInterval_OatLeast(X0,t_b),tc_set(t_b)) = c_SetInterval_OlessThan(X0,t_b),
inference(superposition,[status(thm)],[c_135454,c_4060]) ).
tcf(c_198776,plain,
! [X0: $i,X1: $i] :
( ~ c_in(X0,c_SetInterval_OatLeast(X1,t_b),t_b)
| ~ c_in(X0,c_SetInterval_OlessThan(X1,t_b),t_b) ),
inference(superposition,[status(thm)],[c_198588,c_4127]) ).
tcf(c_198777,plain,
! [X0: $i,X1: $i] :
( c_in(X0,c_SetInterval_OatLeast(X1,t_b),t_b)
| c_in(X0,c_SetInterval_OlessThan(X1,t_b),t_b) ),
inference(superposition,[status(thm)],[c_198588,c_4128]) ).
tcf(c_202057,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X0,t_b)
| c_in(X0,c_SetInterval_OlessThan(X1,t_b),t_b)
| ~ class_Orderings_Oord(t_b) ),
inference(superposition,[status(thm)],[c_198777,c_4076]) ).
tcf(c_202058,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X0,t_b)
| c_in(X0,c_SetInterval_OlessThan(X1,t_b),t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[c_202057,c_135460]) ).
tcf(c_202069,plain,
! [X0: $i,X1: $i] :
( c_less(X1,X0,t_b)
| c_lessequals(X0,X1,t_b)
| ~ class_Orderings_Oord(t_b) ),
inference(superposition,[status(thm)],[c_202058,c_4114]) ).
tcf(c_202070,plain,
! [X0: $i,X1: $i] :
( c_less(X1,X0,t_b)
| c_lessequals(X0,X1,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[c_202069,c_135460]) ).
tcf(c_202100,plain,
c_less(iPr_def_17,iPr_def_10,t_b),
inference(superposition,[status(thm)],[c_202070,c_161125]) ).
tcf(c_209634,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oord(t_b)
| ~ c_less(X0,X1,t_b)
| ~ c_in(X0,c_SetInterval_OatLeast(X1,t_b),t_b) ),
inference(superposition,[status(thm)],[c_4115,c_198776]) ).
tcf(c_209639,plain,
! [X0: $i,X1: $i] :
( ~ c_less(X0,X1,t_b)
| ~ c_in(X0,c_SetInterval_OatLeast(X1,t_b),t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[c_209634,c_135460]) ).
tcf(c_209663,plain,
! [X0: $i,X1: $i] :
( ~ class_Orderings_Oord(t_b)
| ~ c_less(X1,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(superposition,[status(thm)],[c_4077,c_209639]) ).
tcf(c_209668,plain,
! [X0: $i,X1: $i] :
( ~ c_less(X1,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[c_209663,c_135460]) ).
tcf(c_209764,plain,
~ c_less(iPr_def_14,iPr_def_15,t_b),
inference(superposition,[status(thm)],[c_162140,c_209668]) ).
tcf(c_210218,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_minus(X0,X1,X2),iPr_def_10,X2) ),
inference(light_normalisation,[status(thm)],[c_3850,c_135424]) ).
tcf(c_210396,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_135458,c_3852]) ).
tcf(c_210430,plain,
! [X0: $i,X1: $i] :
( c_less(X0,c_uminus(X1,t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_less(c_plus(X0,X1,t_b),iPr_def_10,t_b) ),
inference(superposition,[status(thm)],[c_210396,c_210218]) ).
tcf(c_210450,plain,
! [X0: $i,X1: $i] :
( c_less(X0,c_uminus(X1,t_b),t_b)
| ~ c_less(c_plus(X0,X1,t_b),iPr_def_10,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210430,c_135464]) ).
tcf(c_243980,plain,
( c_less(iPr_def_14,c_uminus(iPr_def_16,t_b),t_b)
| ~ c_less(iPr_def_17,iPr_def_10,t_b) ),
inference(superposition,[status(thm)],[c_135421,c_210450]) ).
tcf(c_243990,plain,
( c_less(iPr_def_14,iPr_def_15,t_b)
| ~ c_less(iPr_def_17,iPr_def_10,t_b) ),
inference(light_normalisation,[status(thm)],[c_243980,c_168181]) ).
tcf(c_243991,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_243990,c_209764,c_202100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA009-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 05:44:07 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 65.02/9.60 % SZS status Started for theBenchmark.p
% 65.02/9.60 % SZS status Unsatisfiable for theBenchmark.p
% 65.02/9.60
% 65.02/9.60 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 65.02/9.60
% 65.02/9.60 % ------ iProver source info
% 65.02/9.60
% 65.02/9.60 % git: date: 2026-07-19 20:42:38 +0200
% 65.02/9.60 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 65.02/9.60 % git: non_committed_changes: false
% 65.02/9.60
% 65.02/9.60 % ------ Parsing...% successful
% 65.02/9.60
% 65.02/9.60
% 65.02/9.60 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 65.02/9.60
% 65.02/9.60 % ------ Preprocessing... sup_sim: 119 sf_s rm: 81 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e sup_sim: 64 sf_s rm: 44 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 44 0s sf_e pe_s pe_e %
% 65.02/9.60
% 65.02/9.60 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 65.02/9.60
% 65.02/9.60 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 65.02/9.60 % ------ Proving...
% 65.02/9.60 % ------ Problem Properties
% 65.02/9.60
% 65.02/9.60 %
% 65.02/9.60 % clauses 1734
% 65.02/9.60 % conjectures 3
% 65.02/9.60 % EPR 238
% 65.02/9.60 % Horn 1536
% 65.02/9.60 % unary 614
% 65.02/9.60 % binary 750
% 65.02/9.60 % lits 3322
% 65.02/9.60 % lits eq 1124
% 65.02/9.60 % fd_pure 0
% 65.02/9.60 % fd_pseudo 0
% 65.02/9.60 % fd_cond 108
% 65.02/9.60 % fd_pseudo_cond 66
% 65.02/9.60 % AC symbols 0
% 65.02/9.60
% 65.02/9.60 % ------ Schedule dynamic 5 is on
% 65.02/9.60
% 65.02/9.60 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 65.02/9.60
% 65.02/9.60
% 65.02/9.60 % ------
% 65.02/9.60 % Current options:
% 65.02/9.60 % ------
% 65.02/9.60
% 65.02/9.60
% 65.02/9.60 %
% 65.02/9.60
% 65.02/9.60 % ------ Proving...
% 65.02/9.60 %
% 65.02/9.60
% 65.02/9.60 % SZS status Unsatisfiable for theBenchmark.p
% 65.02/9.60
% 65.02/9.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 65.02/9.61
% 65.02/9.61
%------------------------------------------------------------------------------