%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL816-1 : 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 : n014.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 02:08:28 PM UTC 2026
% Result : Unsatisfiable 8.04s 1.64s
% Output : CNFRefutation 8.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 24 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-5 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f542,axiom,
! [X2,X3,X0,X1,X4] : c_List_Ofoldl(X0,X1,X2,X3,X4) = c_List_Ofoldr(c_COMBC(X0,X3,X4,X3),c_List_Orev(X2,X4),X1,X4,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr_0) ).
fof(f554,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Type_Otyping(X0,X1,c_List_Ofoldr(c_Type_Otype_OFun,X4,X3,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X0,X2,X4)
| c_Type_Otyping(X0,c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
fof(f586,axiom,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f587,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f588,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f661,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_Type_Otyping(X0,X1,c_List_Ofoldr(c_Type_Otype_OFun,X4,X3,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(X0,X2,X4)
| c_Type_Otyping(X0,c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(X2,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),X3) ),
inference(definition_unfolding,[],[f554,f542]) ).
fof(f671,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(definition_unfolding,[],[f588,f542]) ).
tcf(c_972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Type_Otyping(X0,c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(X4,tc_Lambda_OdB),X1,tc_Lambda_OdB,tc_Lambda_OdB),X3)
| ~ c_Type_Otypings(X0,X4,X2)
| ~ c_Type_Otyping(X0,X1,c_List_Ofoldr(c_Type_Otype_OFun,X2,X3,tc_Type_Otype,tc_Type_Otype)) ),
inference(cnf_transformation,[],[f661]) ).
tcf(c_1002,plain,
c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____),
inference(cnf_transformation,[],[f586]) ).
tcf(c_1003,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(cnf_transformation,[],[f587]) ).
tcf(c_1004,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(cnf_transformation,[],[f671]) ).
tcf(c_4319,plain,
! [X0: $i] :
( c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Ofoldr(c_Type_Otype_OFun,X0,v_T_H____,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),X0) ),
inference(instantiation,[status(thm)],[c_972]) ).
tcf(c_4905,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Ofoldr(c_COMBC(c_Lambda_OdB_OApp,tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Orev(c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),tc_Type_Otype),c_List_Omap(hAPP(c_COMBC(c_Lambda_Olift,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(c_COMBC(hAPP(c_COMBC(c_Lambda_Osubst,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_u____),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_i____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_Ts____) ),
inference(instantiation,[status(thm)],[c_4319]) ).
tcf(c_4906,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4905,c_1004,c_1002,c_1003]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL816-1 : 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 : n014.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 00:32:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 8.04/1.64 % SZS status Started for theBenchmark.p
% 8.04/1.64 % SZS status Unsatisfiable for theBenchmark.p
% 8.04/1.64
% 8.04/1.64 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.04/1.64
% 8.04/1.64 % ------ iProver source info
% 8.04/1.64
% 8.04/1.64 % git: date: 2026-07-19 20:42:38 +0200
% 8.04/1.64 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.04/1.64 % git: non_committed_changes: false
% 8.04/1.64
% 8.04/1.64 % ------ Parsing...% successful
% 8.04/1.64
% 8.04/1.64
% 8.04/1.64 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.04/1.64
% 8.04/1.64 % ------ Preprocessing... sup_sim: 1 pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 1 pe_s pe_e %
% 8.04/1.64
% 8.04/1.64 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 7 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 8.04/1.64
% 8.04/1.64 % ------ Preprocessing...
% 8.04/1.64 % ------ Proving...
% 8.04/1.64 % ------ Problem Properties
% 8.04/1.64
% 8.04/1.64 %
% 8.04/1.64 % clauses 339
% 8.04/1.64 % conjectures 1
% 8.04/1.64 % EPR 31
% 8.04/1.64 % Horn 290
% 8.04/1.64 % unary 129
% 8.04/1.64 % binary 142
% 8.04/1.64 % lits 641
% 8.04/1.64 % lits eq 234
% 8.04/1.64 % fd_pure 0
% 8.04/1.64 % fd_pseudo 0
% 8.04/1.64 % fd_cond 16
% 8.04/1.64 % fd_pseudo_cond 52
% 8.04/1.64 % AC symbols 0
% 8.04/1.64
% 8.04/1.64 % ------ Input Options Time Limit: Unbounded
% 8.04/1.64
% 8.04/1.64
% 8.04/1.64 % ------
% 8.04/1.64 % Current options:
% 8.04/1.64 % ------
% 8.04/1.64
% 8.04/1.64
% 8.04/1.64 %
% 8.04/1.64
% 8.04/1.64 % ------ Proving...
% 8.04/1.64 %
% 8.04/1.64
% 8.04/1.64 % SZS status Unsatisfiable for theBenchmark.p
% 8.04/1.64
% 8.04/1.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.04/1.65
% 8.04/1.65
%------------------------------------------------------------------------------