%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL776-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 02:08:21 PM UTC 2026
% Result : Unsatisfiable 9.13s 4.25s
% Output : CNFRefutation 9.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 29
% Syntax : Number of formulae : 84 ( 64 unt; 14 def)
% Number of atoms : 204 ( 52 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 56 ( 29 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-5 aty)
% Number of variables : 118 ( 0 sgn 118 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
fof(f293,axiom,
! [X2,X0,X1] : c_List_Olist__update(X0,X1,c_List_Onth(X0,X1,X2),X2) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__id_0) ).
fof(f589,axiom,
! [X2,X3,X0,X1] : c_List_Olist__update(c_List_Olist_OCons(X0,X1,X2),c_HOL_Ozero__class_Ozero(tc_nat),X3,X2) = c_List_Olist_OCons(X3,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
fof(f592,axiom,
! [X2,X0,X1] : c_List_Onth(c_List_Olist_OCons(X0,X1,X2),c_HOL_Ozero__class_Ozero(tc_nat),X2) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nth__Cons_H_0) ).
fof(f802,axiom,
! [X0,X1] : c_Type_Otyping(X0,c_Lambda_OdB_OVar(X1),hAPP(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
fof(f803,axiom,
! [X2,X0,X1] :
( ~ c_Type_Otyping(X0,c_Lambda_OdB_OVar(X1),X2)
| hAPP(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
fof(f910,axiom,
! [X2,X0,X1] : c_List_Orotate1(c_List_Olist_OCons(X0,X1,X2),X2) = c_List_Oappend(X1,c_List_Olist_OCons(X0,c_List_Olist_ONil(X2),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rotate__simps_1) ).
fof(f925,axiom,
! [X2,X0,X1] :
( hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,X2,c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_3) ).
fof(f926,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X2,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,X2,c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| c_List_Olist_ONil(tc_Lambda_OdB) = c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(reorient_equations,[],[f925]) ).
fof(f937,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__last_0) ).
fof(f980,axiom,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
fof(f994,axiom,
! [X2,X3,X0,X1,X4,X5] : c_List_Ofoldl(X0,X1,c_List_Olist_OCons(X2,X3,X4),X5,X4) = c_List_Ofoldl(X0,hAPP(hAPP(X0,X1),X2),X3,X5,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
fof(f997,axiom,
! [X2,X3,X0,X1] : c_List_Oappend(c_List_Olist_OCons(X0,X1,X2),X3,X2) = c_List_Olist_OCons(X0,c_List_Oappend(X1,X3,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
fof(f1000,axiom,
! [X2,X3,X0,X1] : c_List_Olist_OCons(X0,c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
fof(f1022,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1023,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1025,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
tcf(c_1102,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Olist__update(X0,X1,c_List_Onth(X0,X1,X2),X2) = X0,
inference(cnf_transformation,[],[f293]) ).
tcf(c_1261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_List_Olist__update(c_List_Olist_OCons(X0,X1,X2),c_HOL_Ozero__class_Ozero(tc_nat),X3,X2) = c_List_Olist_OCons(X3,X1,X2),
inference(cnf_transformation,[],[f589]) ).
tcf(c_1263,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Onth(c_List_Olist_OCons(X0,X1,X2),c_HOL_Ozero__class_Ozero(tc_nat),X2) = X0,
inference(cnf_transformation,[],[f592]) ).
tcf(c_1408,plain,
! [X0: $i,X1: $i] : c_Type_Otyping(X0,c_Lambda_OdB_OVar(X1),hAPP(X0,X1)),
inference(cnf_transformation,[],[f802]) ).
tcf(c_1409,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(X0,X1) = X2 )
| ~ c_Type_Otyping(X0,c_Lambda_OdB_OVar(X1),X2) ),
inference(cnf_transformation,[],[f803]) ).
tcf(c_1488,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Orotate1(c_List_Olist_OCons(X1,X0,X2),X2),
inference(cnf_transformation,[],[f910]) ).
tcf(c_1500,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) = c_List_Olist_ONil(tc_Lambda_OdB) )
| ( c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2) ) ),
inference(cnf_transformation,[],[f926]) ).
tcf(c_1509,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),
inference(cnf_transformation,[],[f937]) ).
tcf(c_1540,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(cnf_transformation,[],[f980]) ).
tcf(c_1551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : c_List_Ofoldl(X0,hAPP(hAPP(X0,X1),X2),X3,X4,X5) = c_List_Ofoldl(X0,X1,c_List_Olist_OCons(X2,X3,X5),X4,X5),
inference(cnf_transformation,[],[f994]) ).
tcf(c_1554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_List_Olist_OCons(X0,c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),
inference(cnf_transformation,[],[f997]) ).
tcf(c_1557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_List_Olist_OCons(X0,c_List_Oappend(X1,X2,X3),X3) = c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),
inference(cnf_transformation,[],[f1000]) ).
tcf(c_1573,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(cnf_transformation,[],[f1022]) ).
tcf(c_1574,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
inference(cnf_transformation,[],[f1023]) ).
tcf(c_1576,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnf_transformation,[],[f1025]) ).
tcf(c_2077,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2),
inference(global_subsumption_just,[status(thm)],[c_1500,c_1509]) ).
tcf(c_7453,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r),c_List_Orotate1(c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_OCons(v_s,v_ss,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(demodulation,[status(thm)],[c_1576,c_1488,c_1551,c_1554]) ).
tcf(c_7646,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Orotate1(c_List_Olist_OCons(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X1),
inference(demodulation,[status(thm)],[c_2077,c_1488]) ).
tcf(c_7647,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r),c_List_Olist_OCons(v_s,v_ss,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(demodulation,[status(thm)],[c_7453,c_7646]) ).
tcf(c_8292,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),c_List_Olist_OCons(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(demodulation,[status(thm)],[c_1540,c_1551]) ).
tcf(c_28293,definition,
iPr_def_10 = c_Lambda_OdB_OAbs(v_r),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_28294,definition,
iPr_def_11 = c_List_Olist_OCons(v_s,v_ss,tc_Lambda_OdB),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_28295,definition,
iPr_def_12 = c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_10,iPr_def_11,tc_Lambda_OdB,tc_Lambda_OdB),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_28296,definition,
iPr_def_13 = hAPP(c_Lambda_OdB_OApp,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_28297,definition,
iPr_def_14 = c_Lambda_OdB_OVar(v_i),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_28298,definition,
iPr_def_15 = hAPP(iPr_def_13,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_28299,definition,
iPr_def_16 = hAPP(c_InductTermi_OIT,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_28303,definition,
iPr_def_20 = hAPP(c_InductTermi_OIT,v_s),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_28304,definition,
iPr_def_21 = c_HOL_Ozero__class_Ozero(tc_nat),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_28305,definition,
iPr_def_22 = c_Lambda_Osubst(v_r,v_s,iPr_def_21),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_28306,definition,
iPr_def_23 = c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_22,v_ss,tc_Lambda_OdB,tc_Lambda_OdB),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_28307,definition,
iPr_def_24 = hAPP(c_Lambda_OdB_OApp,iPr_def_23),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_28308,definition,
iPr_def_25 = hAPP(iPr_def_24,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_28309,definition,
iPr_def_26 = hAPP(c_InductTermi_OIT,iPr_def_25),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_28311,plain,
~ hBOOL(iPr_def_16),
inference(demodulation,[status(thm)],[c_7647,c_28297,c_28294,c_28293,c_28295,c_28296,c_28298,c_28299]) ).
tcf(c_28313,negated_conjecture,
hBOOL(iPr_def_20),
inference(demodulation,[status(thm)],[c_1574,c_28303]) ).
tcf(c_28314,negated_conjecture,
hBOOL(iPr_def_26),
inference(demodulation,[status(thm)],[c_1573,c_28304,c_28305,c_28306,c_28307,c_28308,c_28309]) ).
tcf(c_36802,plain,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),c_List_Olist_OCons(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,iPr_def_21),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(light_normalisation,[status(thm)],[c_8292,c_28304]) ).
tcf(c_36807,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_10,c_List_Olist_OCons(X0,X1,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,X0,iPr_def_21),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(superposition,[status(thm)],[c_28293,c_36802]) ).
tcf(c_36850,plain,
c_Type_Otyping(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(iPr_def_12),iPr_def_13),
inference(superposition,[status(thm)],[c_28296,c_1408]) ).
tcf(c_36851,plain,
c_Type_Otyping(iPr_def_13,c_Lambda_OdB_OVar(iPr_def_14),iPr_def_15),
inference(superposition,[status(thm)],[c_28298,c_1408]) ).
tcf(c_36852,plain,
c_Type_Otyping(c_InductTermi_OIT,c_Lambda_OdB_OVar(iPr_def_15),iPr_def_16),
inference(superposition,[status(thm)],[c_28299,c_1408]) ).
tcf(c_36855,plain,
c_Type_Otyping(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(iPr_def_23),iPr_def_24),
inference(superposition,[status(thm)],[c_28307,c_1408]) ).
tcf(c_36856,plain,
c_Type_Otyping(iPr_def_24,c_Lambda_OdB_OVar(iPr_def_14),iPr_def_25),
inference(superposition,[status(thm)],[c_28308,c_1408]) ).
tcf(c_36857,plain,
c_Type_Otyping(c_InductTermi_OIT,c_Lambda_OdB_OVar(iPr_def_25),iPr_def_26),
inference(superposition,[status(thm)],[c_28309,c_1408]) ).
tcf(c_36895,plain,
! [X0: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_10,c_List_Olist_OCons(v_s,X0,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_s))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_22,X0,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(superposition,[status(thm)],[c_28305,c_36807]) ).
tcf(c_36899,plain,
! [X0: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_10,c_List_Olist_OCons(v_s,X0,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(iPr_def_20)
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_22,X0,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(light_normalisation,[status(thm)],[c_36895,c_28303]) ).
tcf(c_36900,plain,
! [X0: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_10,c_List_Olist_OCons(v_s,X0,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_22,X0,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36899,c_28313]) ).
tcf(c_37285,plain,
! [X0: $i,X1: $i,X2: $i] : c_List_Onth(c_List_Olist_OCons(X0,X1,X2),iPr_def_21,X2) = X0,
inference(light_normalisation,[status(thm)],[c_1263,c_28304]) ).
tcf(c_37286,plain,
c_List_Onth(iPr_def_11,iPr_def_21,tc_Lambda_OdB) = v_s,
inference(superposition,[status(thm)],[c_28294,c_37285]) ).
tcf(c_37307,plain,
c_List_Olist__update(iPr_def_11,iPr_def_21,v_s,tc_Lambda_OdB) = iPr_def_11,
inference(superposition,[status(thm)],[c_37286,c_1102]) ).
tcf(c_37553,plain,
hAPP(c_Lambda_OdB_OApp,iPr_def_12) = iPr_def_13,
inference(superposition,[status(thm)],[c_36850,c_1409]) ).
tcf(c_37554,plain,
hAPP(iPr_def_13,iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_36851,c_1409]) ).
tcf(c_37555,plain,
hAPP(c_InductTermi_OIT,iPr_def_15) = iPr_def_16,
inference(superposition,[status(thm)],[c_36852,c_1409]) ).
tcf(c_37558,plain,
hAPP(c_Lambda_OdB_OApp,iPr_def_23) = iPr_def_24,
inference(superposition,[status(thm)],[c_36855,c_1409]) ).
tcf(c_37559,plain,
hAPP(iPr_def_24,iPr_def_14) = iPr_def_25,
inference(superposition,[status(thm)],[c_36856,c_1409]) ).
tcf(c_37560,plain,
hAPP(c_InductTermi_OIT,iPr_def_25) = iPr_def_26,
inference(superposition,[status(thm)],[c_36857,c_1409]) ).
tcf(c_43044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_List_Olist__update(c_List_Olist_OCons(X0,X1,X2),iPr_def_21,X3,X2) = c_List_Olist_OCons(X3,X1,X2),
inference(light_normalisation,[status(thm)],[c_1261,c_28304]) ).
tcf(c_43048,plain,
! [X0: $i] : c_List_Olist__update(iPr_def_11,iPr_def_21,X0,tc_Lambda_OdB) = c_List_Olist_OCons(X0,v_ss,tc_Lambda_OdB),
inference(superposition,[status(thm)],[c_28294,c_43044]) ).
tcf(c_43054,plain,
c_List_Olist_OCons(v_s,v_ss,tc_Lambda_OdB) = iPr_def_11,
inference(demodulation,[status(thm)],[c_37307,c_43048]) ).
tcf(c_48967,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_10,c_List_Oappend(c_List_Olist_OCons(v_s,X0,tc_Lambda_OdB),X1,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_22,c_List_Oappend(X0,X1,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(superposition,[status(thm)],[c_1557,c_36900]) ).
tcf(c_49283,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_10,c_List_Orotate1(c_List_Olist_OCons(X1,c_List_Olist_OCons(v_s,X0,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_22,c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(superposition,[status(thm)],[c_1488,c_48967]) ).
tcf(c_49336,plain,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_10,c_List_Olist_OCons(v_s,X0,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_22,X0,tc_Lambda_OdB,tc_Lambda_OdB)),X1))) ),
inference(demodulation,[status(thm)],[c_49283,c_1488,c_7646]) ).
tcf(c_49345,plain,
! [X0: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_10,iPr_def_11,tc_Lambda_OdB,tc_Lambda_OdB)),X0)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,iPr_def_22,v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),X0))) ),
inference(superposition,[status(thm)],[c_43054,c_49336]) ).
tcf(c_49347,plain,
! [X0: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(iPr_def_13,X0)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(iPr_def_24,X0))) ),
inference(light_normalisation,[status(thm)],[c_49345,c_28295,c_28306,c_37553,c_37558]) ).
tcf(c_51152,plain,
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(iPr_def_13,iPr_def_14)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,iPr_def_25)) ),
inference(superposition,[status(thm)],[c_37559,c_49347]) ).
tcf(c_51154,plain,
( hBOOL(iPr_def_16)
| ~ hBOOL(iPr_def_26) ),
inference(light_normalisation,[status(thm)],[c_51152,c_37554,c_37555,c_37560]) ).
tcf(c_51155,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_51154,c_28311,c_28314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL776-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 00:30:48 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 9.13/4.25 % SZS status Started for theBenchmark.p
% 9.13/4.25 % SZS status Unsatisfiable for theBenchmark.p
% 9.13/4.25
% 9.13/4.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.13/4.25
% 9.13/4.25 % ------ iProver source info
% 9.13/4.25
% 9.13/4.25 % git: date: 2026-07-19 20:42:38 +0200
% 9.13/4.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.13/4.25 % git: non_committed_changes: false
% 9.13/4.25
% 9.13/4.25 % ------ Parsing...% successful
% 9.13/4.25
% 9.13/4.25
% 9.13/4.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.13/4.25
% 9.13/4.25 % ------ Preprocessing... sup_sim: 44 sf_s rm: 4 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: 18 sf_s rm: 35 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 35 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 35 0s sf_e pe_s pe_e %
% 9.13/4.25
% 9.13/4.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.13/4.25
% 9.13/4.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.13/4.25 % ------ Proving...
% 9.13/4.25 % ------ Problem Properties
% 9.13/4.25
% 9.13/4.25 %
% 9.13/4.25 % clauses 575
% 9.13/4.25 % conjectures 4
% 9.13/4.25 % EPR 23
% 9.13/4.25 % Horn 474
% 9.13/4.25 % unary 195
% 9.13/4.25 % binary 249
% 9.13/4.25 % lits 1109
% 9.13/4.25 % lits eq 471
% 9.13/4.25 % fd_pure 0
% 9.13/4.25 % fd_pseudo 0
% 9.13/4.25 % fd_cond 27
% 9.13/4.25 % fd_pseudo_cond 87
% 9.13/4.25 % AC symbols 0
% 9.13/4.25
% 9.13/4.25 % ------ Schedule dynamic 5 is on
% 9.13/4.25
% 9.13/4.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.13/4.25
% 9.13/4.25
% 9.13/4.25 % ------
% 9.13/4.25 % Current options:
% 9.13/4.25 % ------
% 9.13/4.25
% 9.13/4.25
% 9.13/4.25 %
% 9.13/4.25
% 9.13/4.25 % ------ Proving...
% 9.13/4.25 %
% 9.13/4.25
% 9.13/4.25 % SZS status Unsatisfiable for theBenchmark.p
% 9.13/4.25
% 9.13/4.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.13/4.25
% 9.13/4.25
%------------------------------------------------------------------------------