%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL830-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 01:23:28 PM UTC 2026
% Result : Unsatisfiable 182.82s 24.10s
% Output : CNFRefutation 182.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 29
% Syntax : Number of clauses : 109 ( 64 unt; 6 nHn; 56 RR)
% Number of literals : 168 ( 90 equ; 64 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-5 aty)
% Number of variables : 302 ( 53 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_take__eq__Nil_0,axiom,
( c_List_Otake(X1,X2,X3) != c_List_Olist_ONil(X3)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_List_Olist_ONil(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
cnf(cls_Nil__is__append__conv_1,axiom,
( c_List_Olist_ONil(X1) != c_List_Oappend(X2,X3,X1)
| X3 = c_List_Olist_ONil(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
cnf(cls_list_Osimps_I2_J_0,axiom,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
cnf(cls_diff__self__eq__0_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
cnf(cls_append__eq__conv__conj_0,axiom,
X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
cnf(cls_rev_Osimps_I2_J_0,axiom,
c_List_Orev(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
cnf(cls_length__rev_0,axiom,
c_Nat_Osize__class_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
cnf(cls_drop__0_0,axiom,
c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__0_0) ).
cnf(cls_append__eq__conv__conj_1,axiom,
X1 = c_List_Odrop(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),c_List_Oappend(X2,X1,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
cnf(cls_impossible__Cons_0,axiom,
~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
cnf(cls_append__in__listsp__conv_0,axiom,
( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| c_List_Olistsp(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
cnf(cls_append__in__listsp__conv_1,axiom,
( ~ c_List_Olistsp(X1,c_List_Oappend(X4,X2,X3),X3)
| c_List_Olistsp(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
cnf(cls_take__all_0,axiom,
( ~ c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat)
| c_List_Otake(X1,X2,X3) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__all_0) ).
cnf(cls_nat__le__linear_0,axiom,
( c_lessequals(X2,X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
cnf(cls_rev__append_0,axiom,
c_List_Orev(c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Orev(X1,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
cnf(cls_Cons_I3_J_0,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons_I3_J_0) ).
cnf(cls_rev__swap_0,axiom,
X1 = c_List_Orev(c_List_Orev(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
cnf(cls_append__eq__appendI_0,axiom,
c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
cnf(cls_append__in__listsp__conv_2,axiom,
( ~ c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,X3,X4)
| c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
cnf(cls_append__take__drop__id_0,axiom,
c_List_Oappend(c_List_Otake(X1,X2,X3),c_List_Odrop(X1,X2,X3),X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
cnf(cls_Cons__eq__append__conv_5,axiom,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
cnf(cls_self__append__conv2_1,axiom,
X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
cnf(cls_CHAINED_0,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_Nil__is__rev__conv_1,axiom,
c_List_Olist_ONil(X1) = c_List_Orev(c_List_Olist_ONil(X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
cnf(cls_map__append_0,axiom,
c_List_Omap(X1,c_List_Oappend(X2,X3,X4),X4,X5) = c_List_Oappend(c_List_Omap(X1,X2,X4,X5),c_List_Omap(X1,X3,X4,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).
cnf(cls_map__eq__Cons__conv_3,axiom,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
cnf(cls_Nil__is__map__conv_1,axiom,
c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(c_0_29,plain,
( c_List_Otake(X1,X2,X3) != c_List_Olist_ONil(X3)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_List_Olist_ONil(X3) ),
inference(fof_simplification,[status(thm)],[cls_take__eq__Nil_0]) ).
cnf(c_0_30,plain,
( c_List_Olist_ONil(X1) != c_List_Oappend(X2,X3,X1)
| X3 = c_List_Olist_ONil(X1) ),
inference(fof_simplification,[status(thm)],[cls_Nil__is__append__conv_1]) ).
cnf(c_0_31,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
inference(fof_simplification,[status(thm)],[cls_list_Osimps_I2_J_0]) ).
cnf(c_0_32,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
cls_diff__self__eq__0_0 ).
cnf(c_0_33,plain,
( c_List_Otake(X1,X2,X3) != c_List_Olist_ONil(X3)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X2 = c_List_Olist_ONil(X3) ),
c_0_29 ).
cnf(c_0_34,axiom,
X1 = c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(X1,X3,X2),X2),
cls_append__eq__conv__conj_0 ).
cnf(c_0_35,axiom,
c_List_Orev(c_List_Olist_OCons(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Olist_OCons(X1,c_List_Olist_ONil(X3),X3),X3),
cls_rev_Osimps_I2_J_0 ).
cnf(c_0_36,axiom,
c_Nat_Osize__class_Osize(c_List_Orev(X1,X2),tc_List_Olist(X2)) = c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),
cls_length__rev_0 ).
cnf(c_0_37,plain,
( c_List_Olist_ONil(X1) != c_List_Oappend(X2,X3,X1)
| X3 = c_List_Olist_ONil(X1) ),
c_0_30 ).
cnf(c_0_38,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
c_0_31 ).
cnf(c_0_39,axiom,
c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X1,X2) = X1,
cls_drop__0_0 ).
cnf(c_0_40,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),
inference(rw,[status(thm)],[c_0_32,c_0_32]) ).
cnf(c_0_41,axiom,
X1 = c_List_Odrop(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),c_List_Oappend(X2,X1,X3),X3),
cls_append__eq__conv__conj_1 ).
cnf(c_0_42,plain,
( c_List_Otake(X1,X2,X3) != c_List_Olist_ONil(X3)
| X2 = c_List_Olist_ONil(X3)
| X1 = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat) ),
inference(rw,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_43,plain,
c_List_Otake(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Orev(c_List_Olist_OCons(X3,X1,X2),X2),X2) = c_List_Orev(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_44,plain,
c_List_Orev(c_List_Olist_OCons(X1,X2,X3),X3) != c_List_Olist_ONil(X3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_38]) ).
cnf(c_0_45,plain,
c_List_Odrop(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat),X1,X2) = X1,
inference(rw,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_46,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X2,X2,tc_nat),
inference(spm,[status(thm)],[c_0_40,c_0_40]) ).
cnf(c_0_47,plain,
~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),
inference(fof_simplification,[status(thm)],[cls_impossible__Cons_0]) ).
cnf(c_0_48,plain,
( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| c_List_Olistsp(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[cls_append__in__listsp__conv_0]) ).
cnf(c_0_49,plain,
c_List_Odrop(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_List_Oappend(c_List_Orev(X1,X2),X3,X2),X2) = X3,
inference(spm,[status(thm)],[c_0_41,c_0_36]) ).
cnf(c_0_50,plain,
( c_List_Orev(X1,X2) != c_List_Olist_ONil(X2)
| c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_nat) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_51,plain,
c_List_Odrop(c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),X2,X3) = X2,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),
c_0_47 ).
cnf(c_0_53,plain,
( ~ c_List_Olistsp(X1,c_List_Oappend(X4,X2,X3),X3)
| c_List_Olistsp(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[cls_append__in__listsp__conv_1]) ).
cnf(c_0_54,plain,
( ~ c_List_Olistsp(X1,c_List_Oappend(X2,X4,X3),X3)
| c_List_Olistsp(X1,X2,X3) ),
c_0_48 ).
cnf(c_0_55,plain,
( c_List_Orev(X1,X2) != c_List_Olist_ONil(X2)
| c_List_Oappend(c_List_Orev(X1,X2),X3,X2) = X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_56,plain,
( ~ c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat)
| c_List_Otake(X1,X2,X3) = X2 ),
inference(fof_simplification,[status(thm)],[cls_take__all_0]) ).
cnf(c_0_57,plain,
~ c_lessequals(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,c_List_Orev(X2,X3),X3),tc_List_Olist(X3)),c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),tc_nat),
inference(spm,[status(thm)],[c_0_52,c_0_36]) ).
cnf(c_0_58,axiom,
( c_lessequals(X2,X1,tc_nat)
| c_lessequals(X1,X2,tc_nat) ),
cls_nat__le__linear_0 ).
cnf(c_0_59,plain,
( ~ c_List_Olistsp(X1,c_List_Oappend(X4,X2,X3),X3)
| c_List_Olistsp(X1,X2,X3) ),
c_0_53 ).
cnf(c_0_60,axiom,
c_List_Orev(c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(c_List_Orev(X2,X3),c_List_Orev(X1,X3),X3),
cls_rev__append_0 ).
cnf(c_0_61,plain,
( ~ c_List_Olistsp(X1,X4,X3)
| c_List_Orev(X2,X3) != c_List_Olist_ONil(X3)
| c_List_Olistsp(X1,c_List_Orev(X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
cls_Cons_I3_J_0 ).
cnf(c_0_63,plain,
( ~ c_lessequals(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X1,tc_nat)
| c_List_Otake(X1,X2,X3) = X2 ),
c_0_56 ).
cnf(c_0_64,plain,
c_lessequals(c_Nat_Osize__class_Osize(X1,tc_List_Olist(X2)),c_Nat_Osize__class_Osize(c_List_Olist_OCons(X3,c_List_Orev(X1,X2),X2),tc_List_Olist(X2)),tc_nat),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,plain,
( ~ c_List_Olistsp(X1,c_List_Orev(c_List_Oappend(X2,X4,X3),X3),X3)
| c_List_Olistsp(X1,c_List_Orev(X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,plain,
( c_List_Orev(X1,tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Orev(X1,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,plain,
c_List_Otake(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,c_List_Orev(X2,X3),X3),tc_List_Olist(X3)),X2,X3) = X2,
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,axiom,
X1 = c_List_Orev(c_List_Orev(X1,X2),X2),
cls_rev__swap_0 ).
cnf(c_0_69,axiom,
c_List_Oappend(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Oappend(X1,X2,X4),X3,X4),
cls_append__eq__appendI_0 ).
cnf(c_0_70,plain,
( ~ c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,X3,X4)
| c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(fof_simplification,[status(thm)],[cls_append__in__listsp__conv_2]) ).
cnf(c_0_71,plain,
( c_List_Orev(c_List_Oappend(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Orev(X1,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,axiom,
c_List_Oappend(c_List_Otake(X1,X2,X3),c_List_Odrop(X1,X2,X3),X3) = X2,
cls_append__take__drop__id_0 ).
cnf(c_0_73,plain,
c_List_Otake(c_Nat_Osize__class_Osize(c_List_Olist_OCons(X1,X2,X3),tc_List_Olist(X3)),c_List_Orev(X2,X3),X3) = c_List_Orev(X2,X3),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,axiom,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
cls_Cons__eq__append__conv_5 ).
cnf(c_0_75,plain,
( ~ c_List_Olistsp(X1,c_List_Oappend(X2,c_List_Oappend(X3,X5,X4),X4),X4)
| c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(spm,[status(thm)],[c_0_54,c_0_69]) ).
cnf(c_0_76,plain,
( ~ c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,X3,X4)
| c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
c_0_70 ).
cnf(c_0_77,plain,
( c_List_Orev(X2,tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Orev(c_List_Otake(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
c_List_Otake(c_Nat_Osize__class_Osize(c_List_Oappend(c_List_Olist_OCons(X1,X2,X3),X4,X3),tc_List_Olist(X3)),c_List_Orev(c_List_Oappend(X2,X4,X3),X3),X3) = c_List_Orev(c_List_Oappend(X2,X4,X3),X3),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,axiom,
X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
cls_self__append__conv2_1 ).
cnf(c_0_80,plain,
( ~ c_List_Olistsp(X1,X2,X4)
| ~ c_List_Olistsp(X1,c_List_Oappend(X3,X5,X4),X4)
| c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,plain,
( c_List_Oappend(X1,X2,tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Oappend(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_68]),c_0_68]) ).
cnf(c_0_82,plain,
( c_List_Orev(X1,X3) != c_List_Olist_ONil(X3)
| c_List_Oappend(X1,X2,X3) = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_50]),c_0_51]) ).
cnf(c_0_83,plain,
c_List_Orev(c_List_Oappend(X1,c_List_Orev(X2,X3),X3),X3) = c_List_Oappend(X2,c_List_Orev(X1,X3),X3),
inference(spm,[status(thm)],[c_0_60,c_0_68]) ).
cnf(c_0_84,plain,
c_List_Oappend(c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X3,X2) = c_List_Olist_OCons(X1,X3,X2),
inference(spm,[status(thm)],[c_0_74,c_0_79]) ).
cnf(c_0_85,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Oappend(X2,X3,tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Oappend(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_86,plain,
( c_List_Oappend(X2,c_List_Orev(X1,X3),X3) != c_List_Olist_ONil(X3)
| c_List_Oappend(X1,c_List_Oappend(c_List_Orev(X2,X3),X4,X3),X3) = X4 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_69]) ).
cnf(c_0_87,plain,
( ~ c_List_Olistsp(X1,c_List_Olist_OCons(X4,X2,X3),X3)
| c_List_Olistsp(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_84]) ).
cnf(c_0_88,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Oappend(X3,c_List_Orev(X2,tc_Lambda_OdB),tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Oappend(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86])]) ).
cnf(c_0_89,plain,
( ~ c_List_Olistsp(X1,c_List_Oappend(c_List_Olist_OCons(X5,X2,X4),X3,X4),X4)
| c_List_Olistsp(X1,c_List_Oappend(X2,X3,X4),X4) ),
inference(spm,[status(thm)],[c_0_87,c_0_74]) ).
cnf(c_0_90,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Orev(X2,tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Oappend(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(spm,[status(thm)],[c_0_88,c_0_79]) ).
cnf(c_0_91,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(X3,X1,tc_Lambda_OdB),tc_Lambda_OdB)
| c_List_Orev(X2,tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Oappend(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_92,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
cls_CHAINED_0 ).
cnf(c_0_93,plain,
( c_List_Orev(X1,tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Oappend(c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X1,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_94,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Orev(X2,tc_Lambda_OdB) != c_List_Olist_ONil(tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Oappend(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(spm,[status(thm)],[c_0_80,c_0_93]) ).
cnf(c_0_95,axiom,
c_List_Olist_ONil(X1) = c_List_Orev(c_List_Olist_ONil(X1),X1),
cls_Nil__is__rev__conv_1 ).
cnf(c_0_96,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Oappend(X1,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_97,axiom,
c_List_Omap(X1,c_List_Oappend(X2,X3,X4),X4,X5) = c_List_Oappend(c_List_Omap(X1,X2,X4,X5),c_List_Omap(X1,X3,X4,X5),X5),
cls_map__append_0 ).
cnf(c_0_98,axiom,
c_List_Omap(X1,c_List_Olist_OCons(X2,X3,X4),X4,X5) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Omap(X1,X3,X4,X5),X5),
cls_map__eq__Cons__conv_3 ).
cnf(c_0_99,axiom,
c_List_Olist_ONil(X1) = c_List_Omap(X2,c_List_Olist_ONil(X3),X3,X1),
cls_Nil__is__map__conv_1 ).
cnf(c_0_100,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_101,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Oappend(X1,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_102,plain,
c_List_Omap(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3,X4) = c_List_Olist_OCons(hAPP(X1,X2),c_List_Olist_ONil(X4),X4),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_103,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
cls_COMBC__def_0 ).
cnf(c_0_104,plain,
( ~ c_List_Olistsp(X1,c_List_Olist_OCons(X2,X4,X3),X3)
| c_List_Olistsp(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(X3),X3),X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_84]) ).
cnf(c_0_105,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
c_0_100 ).
cnf(c_0_106,plain,
( ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst,X1),v_u____),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(X1,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_84]),c_0_102]),c_0_103]),c_0_103]) ).
cnf(c_0_107,plain,
c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(spm,[status(thm)],[c_0_104,c_0_92]) ).
cnf(c_0_108,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL830-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 01:08:31 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.46 Running first-order theorem proving
% 0.17/0.46 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 182.82/24.10 % Version: 3.5.1
% 182.82/24.10 % Preprocessing class: FSLMSMSMSSSNFFN.
% 182.82/24.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 182.82/24.10 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 182.82/24.10 % Starting new_bool_3 with 600s (2) cores
% 182.82/24.10 % Starting new_bool_1 with 300s (1) cores
% 182.82/24.10 % Starting sh5l with 300s (1) cores
% 182.82/24.10 % new_bool_3 with pid 3065471 completed with status 0
% 182.82/24.10 % Result found by new_bool_3
% 182.82/24.10 % Preprocessing class: FSLMSMSMSSSNFFN.
% 182.82/24.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 182.82/24.10 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 182.82/24.10 % Starting new_bool_3 with 600s (2) cores
% 182.82/24.10 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 182.82/24.10 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 182.82/24.10 % Search class: FGUSM-FSLM32-MFFFFFNN
% 182.82/24.10 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 182.82/24.10 % Starting SubtermCWHack with 61s (1) cores
% 182.82/24.10 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 182.82/24.10 % SAT001_MinMin_p005000_rr_RG with pid 3065479 completed with status 0
% 182.82/24.10 % Result found by SAT001_MinMin_p005000_rr_RG
% 182.82/24.10 % Preprocessing class: FSLMSMSMSSSNFFN.
% 182.82/24.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 182.82/24.10 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 182.82/24.10 % Starting new_bool_3 with 600s (2) cores
% 182.82/24.10 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 182.82/24.10 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 182.82/24.10 % Search class: FGUSM-FSLM32-MFFFFFNN
% 182.82/24.10 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 182.82/24.10 % Starting SubtermCWHack with 61s (1) cores
% 182.82/24.10 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 182.82/24.10 % Preprocessing time : 0.007 s
% 182.82/24.10 % Presaturation interreduction done
% 182.82/24.10
% 182.82/24.10 % Proof found!
% 182.82/24.10 % SZS status Unsatisfiable
% 182.82/24.10 % SZS output start CNFRefutation
% See solution above
% 182.82/24.11 % Parsed axioms : 483
% 182.82/24.11 % Removed by relevancy pruning/SinE : 220
% 182.82/24.11 % Initial clauses : 263
% 182.82/24.11 % Removed in clause preprocessing : 0
% 182.82/24.11 % Initial clauses in saturation : 263
% 182.82/24.11 % Processed clauses : 48271
% 182.82/24.11 % ...of these trivial : 521
% 182.82/24.11 % ...subsumed : 42695
% 182.82/24.11 % ...remaining for further processing : 5055
% 182.82/24.11 % Other redundant clauses eliminated : 21661
% 182.82/24.11 % Clauses deleted for lack of memory : 0
% 182.82/24.11 % Backward-subsumed : 380
% 182.82/24.11 % Backward-rewritten : 104
% 182.82/24.11 % Generated clauses : 811088
% 182.82/24.11 % ...of the previous two non-redundant : 711666
% 182.82/24.11 % ...aggressively subsumed : 0
% 182.82/24.11 % Contextual simplify-reflections : 54
% 182.82/24.11 % Paramodulations : 789272
% 182.82/24.11 % Factorizations : 54
% 182.82/24.11 % NegExts : 0
% 182.82/24.11 % Equation resolutions : 21762
% 182.82/24.11 % Disequality decompositions : 0
% 182.82/24.11 % Total rewrite steps : 571993
% 182.82/24.11 % ...of those cached : 509250
% 182.82/24.11 % Propositional unsat checks : 1
% 182.82/24.11 % Propositional check models : 0
% 182.82/24.11 % Propositional check unsatisfiable : 0
% 182.82/24.11 % Propositional clauses : 0
% 182.82/24.11 % Propositional clauses after purity: 0
% 182.82/24.11 % Propositional unsat core size : 0
% 182.82/24.11 % Propositional preprocessing time : 0.000
% 182.82/24.11 % Propositional encoding time : 2.251
% 182.82/24.11 % Propositional solver time : 1.225
% 182.82/24.11 % Success case prop preproc time : 0.000
% 182.82/24.11 % Success case prop encoding time : 0.000
% 182.82/24.11 % Success case prop solver time : 0.000
% 182.82/24.11 % Current number of processed clauses : 4357
% 182.82/24.11 % Positive orientable unit clauses : 654
% 182.82/24.11 % Positive unorientable unit clauses: 84
% 182.82/24.11 % Negative unit clauses : 592
% 182.82/24.11 % Non-unit-clauses : 3027
% 182.82/24.11 % Current number of unprocessed clauses: 661577
% 182.82/24.11 % ...number of literals in the above : 1573446
% 182.82/24.11 % Current number of archived formulas : 0
% 182.82/24.11 % Current number of archived clauses : 694
% 182.82/24.11 % Clause-clause subsumption calls (NU) : 2864526
% 182.82/24.11 % Rec. Clause-clause subsumption calls : 1910953
% 182.82/24.11 % Non-unit clause-clause subsumptions : 23271
% 182.82/24.11 % Unit Clause-clause subsumption calls : 358942
% 182.82/24.11 % Rewrite failures with RHS unbound : 0
% 182.82/24.11 % BW rewrite match attempts : 3681
% 182.82/24.11 % BW rewrite match successes : 287
% 182.82/24.11 % Condensation attempts : 0
% 182.82/24.11 % Condensation successes : 0
% 182.82/24.11 % Termbank termtop insertions : 22184126
% 182.82/24.11 % Search garbage collected termcells : 1350
% 182.82/24.11
% 182.82/24.11 % -------------------------------------------------
% 182.82/24.11 % User time : 22.186 s
% 182.82/24.11 % System time : 0.757 s
% 182.82/24.11 % Total time : 22.943 s
% 182.82/24.11 % Maximum resident set size: 4472 pages
% 182.82/24.11
% 182.82/24.11 % -------------------------------------------------
% 182.82/24.11 % User time : 42.804 s
% 182.82/24.11 % System time : 1.405 s
% 182.82/24.11 % Total time : 44.208 s
% 182.82/24.11 % Maximum resident set size: 4864 pages
% 182.82/24.11 % E exiting
%------------------------------------------------------------------------------