%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SCT024-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Thu Sep 24 02:08:12 PM UTC 2026
% Result : Unsatisfiable 73.97s 11.31s
% Output : CNFRefutation 73.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 26
% Syntax : Number of clauses : 93 ( 38 unt; 4 nHn; 52 RR)
% Number of literals : 162 ( 41 equ; 71 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-5 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-4 aty)
% Number of variables : 178 ( 53 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_inf1E_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X4,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
cnf(cls_inf__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_top__fun__eq_0,axiom,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_sup__top__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_inf__sup__absorb_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
cnf(cls_UNIV__eq__I_0,axiom,
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__eq__I_0) ).
cnf(cls_sup__top__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_mem__def_0,axiom,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_conjecture_3,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_8,negated_conjecture,
( ~ c_Relation_Otrans(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
cnf(cls_in__rel__def_1,axiom,
( ~ hBOOL(c_in(c_Pair(X2,X3,X4,X5),X1,tc_prod(X4,X5)))
| c_FunDef_Oin__rel(X1,X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_4,negated_conjecture,
~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_in__rel__def_0,axiom,
( ~ c_FunDef_Oin__rel(X5,X1,X2,X3,X4)
| hBOOL(c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).
cnf(cls_irrefl__def_0,axiom,
( ~ c_Relation_Oirrefl(X3,X2)
| ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
cnf(c_0_26,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X4,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_inf1E_1]) ).
cnf(c_0_27,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
inference(fof_simplification,[status(thm)],[cls_inf__fun__eq_0]) ).
cnf(c_0_28,plain,
( ~ hBOOL(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,tc_fun(X4,tc_bool)),X1),X2))
| hBOOL(hAPP(X1,X2)) ),
c_0_26 ).
cnf(c_0_29,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),X1),hAPP(X3,v_x)) ),
c_0_27 ).
cnf(c_0_30,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_31,plain,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_top__fun__eq_0]) ).
cnf(c_0_32,plain,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),tc_bool),hAPP(X1,v_x)))
| hBOOL(hAPP(X1,v_x)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_33,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_34,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_sup__top__left_0]) ).
cnf(c_0_35,plain,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1) ),
c_0_31 ).
cnf(c_0_36,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_37,plain,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(X2,v_x),tc_bool),X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_inf__sup__absorb_0]) ).
cnf(c_0_39,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_1]) ).
cnf(c_0_40,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(X1),X1),X2) = c_Orderings_Otop__class_Otop(X1) ),
c_0_34 ).
cnf(c_0_41,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_42,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_43,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,plain,
( ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_33]) ).
cnf(c_0_45,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3)) = X2 ),
c_0_38 ).
cnf(c_0_46,plain,
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_UNIV__eq__I_0]) ).
cnf(c_0_47,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(c_in(X1,X2,X3)) ),
c_0_39 ).
cnf(c_0_48,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
hBOOL(c_Orderings_Otop__class_Otop(tc_bool)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1) ),
inference(fof_simplification,[status(thm)],[cls_sup__top__right_0]) ).
cnf(c_0_51,plain,
( ~ hBOOL(X1)
| hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_30])]) ).
cnf(c_0_52,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2) ),
inference(fof_simplification,[status(thm)],[cls_inf__sup__aci_I5_J_0]) ).
cnf(c_0_53,plain,
( ~ hBOOL(c_in(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1),X2,X1))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2 ),
c_0_46 ).
cnf(c_0_54,plain,
hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_55,plain,
( ~ class_Lattices_Obounded__lattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1) ),
c_0_50 ).
cnf(c_0_56,plain,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2 ),
inference(fof_simplification,[status(thm)],[cls_sup__idem_0]) ).
cnf(c_0_57,plain,
( ~ hBOOL(X2)
| hBOOL(c_in(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool),X3)) ),
inference(spm,[status(thm)],[c_0_47,c_0_51]) ).
cnf(c_0_58,plain,
( ~ class_Lattices_Olattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X3) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(X3,X1),X2) ),
c_0_52 ).
cnf(c_0_59,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_55,c_0_41]) ).
cnf(c_0_61,plain,
( ~ class_Lattices_Oupper__semilattice(X1)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(X2,X1),X2) = X2 ),
c_0_56 ).
cnf(c_0_62,plain,
( ~ hBOOL(X2)
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X2,tc_bool) ),
inference(spm,[status(thm)],[c_0_53,c_0_57]) ).
cnf(c_0_63,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2) = c_Orderings_Otop__class_Otop(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_30])]) ).
cnf(c_0_64,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_65,plain,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_mem__def_0]) ).
cnf(c_0_66,plain,
( ~ hBOOL(X1)
| c_Orderings_Otop__class_Otop(tc_bool) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_64])]) ).
cnf(c_0_67,plain,
( ~ hBOOL(c_in(X2,X1,X3))
| hBOOL(hAPP(X1,X2)) ),
c_0_65 ).
cnf(c_0_68,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
cls_conjecture_3 ).
cnf(c_0_69,negated_conjecture,
( ~ c_Relation_Otrans(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_8]) ).
cnf(c_0_70,plain,
( ~ hBOOL(X1)
| ~ hBOOL(X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_66,c_0_66]) ).
cnf(c_0_71,negated_conjecture,
hBOOL(hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,plain,
( ~ hBOOL(c_in(c_Pair(X2,X3,X4,X5),X1,tc_prod(X4,X5)))
| c_FunDef_Oin__rel(X1,X2,X3,X4,X5) ),
inference(fof_simplification,[status(thm)],[cls_in__rel__def_1]) ).
cnf(c_0_73,negated_conjecture,
( ~ c_Relation_Otrans(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Oirrefl(hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(X3,v_Pa(X3)),tc_Arrow__Order__Mirabelle_Oalt)
| ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X3,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(X3),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
c_0_69 ).
cnf(c_0_74,negated_conjecture,
c_Relation_Otrans(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_0 ).
cnf(c_0_75,negated_conjecture,
c_Relation_Ototal__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_2 ).
cnf(c_0_76,negated_conjecture,
c_Relation_Oirrefl(hAPP(v_P,X1),tc_Arrow__Order__Mirabelle_Oalt),
cls_conjecture_1 ).
cnf(c_0_77,negated_conjecture,
( ~ hBOOL(X1)
| hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = X1 ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_78,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),X1)),
inference(spm,[status(thm)],[c_0_47,c_0_71]) ).
cnf(c_0_79,negated_conjecture,
~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(fof_simplification,[status(thm)],[cls_conjecture_4]) ).
cnf(c_0_80,plain,
( ~ hBOOL(c_in(c_Pair(X2,X3,X4,X5),X1,tc_prod(X4,X5)))
| c_FunDef_Oin__rel(X1,X2,X3,X4,X5) ),
c_0_72 ).
cnf(c_0_81,negated_conjecture,
( ~ hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| hBOOL(c_in(c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_76])]) ).
cnf(c_0_82,negated_conjecture,
c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),X1) = hAPP(hAPP(v_P,v_i),c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
~ hBOOL(c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F(v_P),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
c_0_79 ).
cnf(c_0_84,plain,
( ~ c_FunDef_Oin__rel(X5,X1,X2,X3,X4)
| hBOOL(c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))) ),
inference(fof_simplification,[status(thm)],[cls_in__rel__def_0]) ).
cnf(c_0_85,negated_conjecture,
c_FunDef_Oin__rel(hAPP(v_P,v_i),v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
inference(spm,[status(thm)],[c_0_80,c_0_68]) ).
cnf(c_0_86,negated_conjecture,
v_b = v_a,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_71])]),c_0_83]) ).
cnf(c_0_87,plain,
( ~ c_Relation_Oirrefl(X3,X2)
| ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))) ),
inference(fof_simplification,[status(thm)],[cls_irrefl__def_0]) ).
cnf(c_0_88,plain,
( ~ c_FunDef_Oin__rel(X5,X1,X2,X3,X4)
| hBOOL(c_in(c_Pair(X1,X2,X3,X4),X5,tc_prod(X3,X4))) ),
c_0_84 ).
cnf(c_0_89,negated_conjecture,
c_FunDef_Oin__rel(hAPP(v_P,v_i),v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),
inference(rw,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,plain,
( ~ c_Relation_Oirrefl(X3,X2)
| ~ hBOOL(c_in(c_Pair(X1,X1,X2,X2),X3,tc_prod(X2,X2))) ),
c_0_87 ).
cnf(c_0_91,negated_conjecture,
hBOOL(c_in(c_Pair(v_a,v_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P,v_i),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_76])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT024-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n004.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 04:26:34 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.48 Running first-order theorem proving
% 0.17/0.48 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 73.97/11.31 % Version: 3.5.1
% 73.97/11.31 % Preprocessing class: FSLMSMSMSSSNFFN.
% 73.97/11.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.97/11.31 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 73.97/11.31 % Starting new_bool_3 with 600s (2) cores
% 73.97/11.31 % Starting new_bool_1 with 300s (1) cores
% 73.97/11.31 % Starting sh5l with 300s (1) cores
% 73.97/11.31 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 2242124 completed with status 0
% 73.97/11.31 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 73.97/11.31 % Preprocessing class: FSLMSMSMSSSNFFN.
% 73.97/11.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.97/11.31 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 73.97/11.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 73.97/11.31 % No SInE strategy applied
% 73.97/11.31 % Search class: FGHSM-FSLM32-DFFFFFNN
% 73.97/11.31 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 73.97/11.31 % Starting SubtermCWHack with 109s (1) cores
% 73.97/11.31 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 73.97/11.31 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 73.97/11.31 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 73.97/11.31 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 2242133 completed with status 0
% 73.97/11.31 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 73.97/11.31 % Preprocessing class: FSLMSMSMSSSNFFN.
% 73.97/11.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.97/11.31 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 73.97/11.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 73.97/11.31 % No SInE strategy applied
% 73.97/11.31 % Search class: FGHSM-FSLM32-DFFFFFNN
% 73.97/11.31 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 73.97/11.31 % Starting SubtermCWHack with 109s (1) cores
% 73.97/11.31 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 73.97/11.31 % Preprocessing time : 0.018 s
% 73.97/11.31 % Presaturation interreduction done
% 73.97/11.31
% 73.97/11.31 % Proof found!
% 73.97/11.31 % SZS status Unsatisfiable
% 73.97/11.31 % SZS output start CNFRefutation
% See solution above
% 73.97/11.31 % Parsed axioms : 713
% 73.97/11.31 % Removed by relevancy pruning/SinE : 0
% 73.97/11.31 % Initial clauses : 713
% 73.97/11.31 % Removed in clause preprocessing : 4
% 73.97/11.31 % Initial clauses in saturation : 709
% 73.97/11.31 % Processed clauses : 29064
% 73.97/11.31 % ...of these trivial : 851
% 73.97/11.31 % ...subsumed : 20981
% 73.97/11.31 % ...remaining for further processing : 7232
% 73.97/11.31 % Other redundant clauses eliminated : 510
% 73.97/11.31 % Clauses deleted for lack of memory : 0
% 73.97/11.31 % Backward-subsumed : 431
% 73.97/11.31 % Backward-rewritten : 468
% 73.97/11.31 % Generated clauses : 340042
% 73.97/11.31 % ...of the previous two non-redundant : 316670
% 73.97/11.31 % ...aggressively subsumed : 0
% 73.97/11.31 % Contextual simplify-reflections : 13
% 73.97/11.31 % Paramodulations : 339410
% 73.97/11.31 % Factorizations : 10
% 73.97/11.31 % NegExts : 0
% 73.97/11.31 % Equation resolutions : 622
% 73.97/11.31 % Disequality decompositions : 0
% 73.97/11.31 % Total rewrite steps : 84706
% 73.97/11.31 % ...of those cached : 78093
% 73.97/11.31 % Propositional unsat checks : 0
% 73.97/11.31 % Propositional check models : 0
% 73.97/11.31 % Propositional check unsatisfiable : 0
% 73.97/11.31 % Propositional clauses : 0
% 73.97/11.31 % Propositional clauses after purity: 0
% 73.97/11.31 % Propositional unsat core size : 0
% 73.97/11.31 % Propositional preprocessing time : 0.000
% 73.97/11.31 % Propositional encoding time : 0.000
% 73.97/11.31 % Propositional solver time : 0.000
% 73.97/11.31 % Success case prop preproc time : 0.000
% 73.97/11.31 % Success case prop encoding time : 0.000
% 73.97/11.31 % Success case prop solver time : 0.000
% 73.97/11.31 % Current number of processed clauses : 5737
% 73.97/11.31 % Positive orientable unit clauses : 511
% 73.97/11.31 % Positive unorientable unit clauses: 17
% 73.97/11.31 % Negative unit clauses : 133
% 73.97/11.31 % Non-unit-clauses : 5076
% 73.97/11.31 % Current number of unprocessed clauses: 283239
% 73.97/11.31 % ...number of literals in the above : 943229
% 73.97/11.31 % Current number of archived formulas : 0
% 73.97/11.31 % Current number of archived clauses : 1497
% 73.97/11.31 % Clause-clause subsumption calls (NU) : 3922426
% 73.97/11.31 % Rec. Clause-clause subsumption calls : 1071770
% 73.97/11.31 % Non-unit clause-clause subsumptions : 18069
% 73.97/11.31 % Unit Clause-clause subsumption calls : 47248
% 73.97/11.31 % Rewrite failures with RHS unbound : 65
% 73.97/11.31 % BW rewrite match attempts : 2274
% 73.97/11.31 % BW rewrite match successes : 471
% 73.97/11.31 % Condensation attempts : 0
% 73.97/11.31 % Condensation successes : 0
% 73.97/11.31 % Termbank termtop insertions : 6508991
% 73.97/11.31 % Search garbage collected termcells : 1251
% 73.97/11.31
% 73.97/11.31 % -------------------------------------------------
% 73.97/11.31 % User time : 10.244 s
% 73.97/11.31 % System time : 0.282 s
% 73.97/11.31 % Total time : 10.526 s
% 73.97/11.31 % Maximum resident set size: 5012 pages
% 73.97/11.31
% 73.97/11.31 % -------------------------------------------------
% 73.97/11.31 % User time : 40.927 s
% 73.97/11.31 % System time : 1.348 s
% 73.97/11.31 % Total time : 42.275 s
% 73.97/11.31 % Maximum resident set size: 5120 pages
% 73.97/11.31 % E exiting
%------------------------------------------------------------------------------