%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL786-1 : 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 : n009.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 02:08:22 PM UTC 2026
% Result : Unsatisfiable 30.56s 13.33s
% Output : CNFRefutation 30.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 41 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 25 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-5 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f348,axiom,
! [X2,X3,X0,X1,X4] : c_List_Ofoldr(X0,X1,X2,X3,X4) = c_List_Ofoldl(c_COMBC(X0,X3,X4,X4),X2,c_List_Orev(X1,X3),X4,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__foldl_0) ).
fof(f539,axiom,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X0),c_List_Ofoldl(c_Lambda_OdB_OApp,X3,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2))
| c_Type_Otypings(X0,X1,c_Type_Osko__Type__Xlist__app__typeD__1__1(X2,X0,X3,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
fof(f562,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).
fof(f572,axiom,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),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____,v_i____,v_T____,tc_Type_Otype),v_as____,X0)
| v_thesis____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
fof(f601,axiom,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X0),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X2))
| hBOOL(hAPP(hAPP(c_Type_Otyping(X0),X1),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X2,X0,X1,X3),X2,tc_Type_Otype,tc_Type_Otype))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
fof(f608,axiom,
hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f609,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f644,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(X0,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,X0)
| v_thesis____ ),
inference(definition_unfolding,[],[f572,f562,f348]) ).
fof(f649,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X0),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X3,tc_Lambda_OdB,tc_Lambda_OdB)),X2))
| hBOOL(hAPP(hAPP(c_Type_Otyping(X0),X1),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X2,c_List_Orev(c_Type_Osko__Type__Xlist__app__typeD__1__1(X2,X0,X1,X3),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))) ),
inference(definition_unfolding,[],[f601,f348]) ).
fof(f651,plain,
hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
inference(definition_unfolding,[],[f608,f562]) ).
tcf(c_943,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Type_Otypings(X0,X2,c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X0,X1,X2))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X0),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(cnf_transformation,[],[f539]) ).
tcf(c_969,plain,
! [X0: $i] :
( v_thesis____
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,X0)
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(X0,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))) ),
inference(cnf_transformation,[],[f644]) ).
tcf(c_995,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(c_Type_Otyping(X0),X1),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),X3,c_List_Orev(c_Type_Osko__Type__Xlist__app__typeD__1__1(X3,X0,X1,X2),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(X0),c_List_Ofoldl(c_Lambda_OdB_OApp,X1,X2,tc_Lambda_OdB,tc_Lambda_OdB)),X3)) ),
inference(cnf_transformation,[],[f649]) ).
tcf(c_1002,plain,
hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
inference(cnf_transformation,[],[f651]) ).
tcf(c_1003,negated_conjecture,
~ v_thesis____,
inference(cnf_transformation,[],[f609]) ).
tcf(c_1311,plain,
! [X0: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(X0,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,X0) ),
inference(global_subsumption_just,[status(thm)],[c_969,c_1003,c_969]) ).
tcf(c_1312,plain,
! [X0: $i] :
( ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,X0)
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(X0,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))) ),
inference(renaming,[status(thm)],[c_1311]) ).
tcf(c_7553,plain,
! [X0: $i] :
( ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(X0,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,X0) ),
inference(prop_impl_just,[status(thm)],[c_1312]) ).
tcf(c_7554,plain,
! [X0: $i] :
( ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,X0)
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(X0,tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))) ),
inference(renaming,[status(thm)],[c_7553]) ).
tcf(c_20986,plain,
( c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),v_as____))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)) ),
inference(instantiation,[status(thm)],[c_943]) ).
tcf(c_21790,plain,
( hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),v_as____),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype)))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)) ),
inference(instantiation,[status(thm)],[c_995]) ).
tcf(c_23137,plain,
( ~ c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),v_as____))
| ~ hBOOL(hAPP(hAPP(c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldl(c_COMBC(c_Type_Otype_OFun,tc_Type_Otype,tc_Type_Otype,tc_Type_Otype),v_T_H____,c_List_Orev(c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T_H____,c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),v_as____),tc_Type_Otype),tc_Type_Otype,tc_Type_Otype))) ),
inference(instantiation,[status(thm)],[c_7554]) ).
tcf(c_23138,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_23137,c_21790,c_20986,c_1002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL786-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.37 % Computer : n009.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Thu Sep 24 00:30:04 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 30.56/13.33 % SZS status Started for theBenchmark.p
% 30.56/13.33 % SZS status Unsatisfiable for theBenchmark.p
% 30.56/13.33
% 30.56/13.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 30.56/13.33
% 30.56/13.33 % ------ iProver source info
% 30.56/13.33
% 30.56/13.33 % git: date: 2026-07-19 20:42:38 +0200
% 30.56/13.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 30.56/13.33 % git: non_committed_changes: false
% 30.56/13.33
% 30.56/13.33 % ------ Parsing...% successful
% 30.56/13.33
% 30.56/13.33
% 30.56/13.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 30.56/13.33
% 30.56/13.33 % ------ Preprocessing... sup_sim: 36 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 3 sf_s rm: 15 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 15 0s sf_e pe_s pe_e %
% 30.56/13.33
% 30.56/13.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 30.56/13.33
% 30.56/13.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 30.56/13.33 % ------ Proving...
% 30.56/13.33 % ------ Problem Properties
% 30.56/13.33
% 30.56/13.33 %
% 30.56/13.33 % clauses 317
% 30.56/13.33 % conjectures 0
% 30.56/13.33 % EPR 13
% 30.56/13.33 % Horn 277
% 30.56/13.33 % unary 126
% 30.56/13.33 % binary 134
% 30.56/13.33 % lits 575
% 30.56/13.33 % lits eq 278
% 30.56/13.33 % fd_pure 0
% 30.56/13.33 % fd_pseudo 0
% 30.56/13.33 % fd_cond 12
% 30.56/13.33 % fd_pseudo_cond 55
% 30.56/13.33 % AC symbols 0
% 30.56/13.33
% 30.56/13.33 % ------ Input Options Time Limit: Unbounded
% 30.56/13.33
% 30.56/13.33
% 30.56/13.33 % ------
% 30.56/13.33 % Current options:
% 30.56/13.33 % ------
% 30.56/13.33
% 30.56/13.33
% 30.56/13.33 %
% 30.56/13.33
% 30.56/13.33 % ------ Proving...
% 30.56/13.33 %
% 30.56/13.33
% 30.56/13.33 % SZS status Unsatisfiable for theBenchmark.p
% 30.56/13.33
% 30.56/13.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 30.56/13.33
% 30.56/13.33
%------------------------------------------------------------------------------