%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL835-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 02:08:32 PM UTC 2026
% Result : Unsatisfiable 6.03s 2.28s
% Output : CNFRefutation 6.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 23 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-5 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f491,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/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
fof(f503,axiom,
! [X2,X3,X0,X1] :
( ~ c_Type_Otyping(X0,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X3),X1))
| c_Type_Otyping(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
fof(f563,axiom,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f564,axiom,
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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f565,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tcf(c_543,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(cnf_transformation,[],[f565]) ).
tcf(c_588,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Type_Otyping(X2,X1,X3)
| ~ c_Type_Otyping(X2,X0,X3)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X1)) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_597,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(cnf_transformation,[],[f563]) ).
tcf(c_600,plain,
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_OAbs(v_r____)),v_a____),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(cnf_transformation,[],[f564]) ).
tcf(c_743,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,[],[f491]) ).
tcf(c_2071,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____),
inference(demodulation,[status(thm)],[c_600,c_743]) ).
tcf(c_2207,plain,
hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))),
inference(demodulation,[status(thm)],[c_597,c_743]) ).
tcf(c_9669,plain,
! [X0: $i,X1: $i] :
( c_Type_Otyping(X0,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),X1)
| ~ c_Type_Otyping(X0,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),X1)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(instantiation,[status(thm)],[c_588]) ).
tcf(c_22534,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_r____),v_a____),c_HOL_Ozero__class_Ozero(tc_nat)),v_as____,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(instantiation,[status(thm)],[c_9669]) ).
tcf(c_22535,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_22534,c_2207,c_2071,c_543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL835-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n007.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 00:32:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 6.03/2.28 % SZS status Started for theBenchmark.p
% 6.03/2.28 % SZS status Unsatisfiable for theBenchmark.p
% 6.03/2.28
% 6.03/2.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.03/2.28
% 6.03/2.28 % ------ iProver source info
% 6.03/2.28
% 6.03/2.28 % git: date: 2026-07-19 20:42:38 +0200
% 6.03/2.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.03/2.28 % git: non_committed_changes: false
% 6.03/2.28
% 6.03/2.28 % ------ Parsing...% successful
% 6.03/2.28
% 6.03/2.28
% 6.03/2.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.03/2.28
% 6.03/2.28 % ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 6.03/2.28
% 6.03/2.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.03/2.28
% 6.03/2.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.03/2.28 % ------ Proving...
% 6.03/2.28 % ------ Problem Properties
% 6.03/2.28
% 6.03/2.28 %
% 6.03/2.28 % clauses 136
% 6.03/2.28 % conjectures 1
% 6.03/2.28 % EPR 3
% 6.03/2.28 % Horn 126
% 6.03/2.28 % unary 46
% 6.03/2.28 % binary 65
% 6.03/2.28 % lits 259
% 6.03/2.28 % lits eq 115
% 6.03/2.28 % fd_pure 0
% 6.03/2.28 % fd_pseudo 0
% 6.03/2.28 % fd_cond 11
% 6.03/2.28 % fd_pseudo_cond 31
% 6.03/2.28 % AC symbols 0
% 6.03/2.28
% 6.03/2.28 % ------ Schedule dynamic 5 is on
% 6.03/2.28
% 6.03/2.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.03/2.28
% 6.03/2.28
% 6.03/2.28 % ------
% 6.03/2.28 % Current options:
% 6.03/2.28 % ------
% 6.03/2.28
% 6.03/2.28
% 6.03/2.28 %
% 6.03/2.28
% 6.03/2.28 % ------ Proving...
% 6.03/2.28 %
% 6.03/2.28
% 6.03/2.28 % SZS status Unsatisfiable for theBenchmark.p
% 6.03/2.28
% 6.03/2.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.03/2.28
% 6.03/2.28
%------------------------------------------------------------------------------