%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL836-1 : 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 : n019.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 4.85s 1.35s
% Output : CNFRefutation 4.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-5 aty)
% Number of variables : 9 ( 0 sgn 9 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f695,axiom,
! [X2,X3,X0,X1] :
( ~ c_Type_Otyping(c_Type_Oshift(X2,X1,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),X3)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| ~ c_Type_Otyping(X2,X0,v_T____)
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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)),X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SI1_0) ).
fof(f704,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f705,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f706,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(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_CHAINED_0_02) ).
fof(f707,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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_u____),v_i____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tcf(c_1172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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)),X3),X1)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X3))
| ~ c_Type_Otyping(X0,X3,v_T____)
| ~ c_Type_Otyping(c_Type_Oshift(X0,X1,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),X2) ),
inference(cnf_transformation,[],[f695]) ).
tcf(c_1181,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(cnf_transformation,[],[f704]) ).
tcf(c_1182,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(cnf_transformation,[],[f705]) ).
tcf(c_1183,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____),
inference(cnf_transformation,[],[f706]) ).
tcf(c_1184,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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_u____),v_i____))),
inference(cnf_transformation,[],[f707]) ).
tcf(c_1462,plain,
! [X0: $i] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,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)),X0),v_i____)))
| ~ c_Type_Otyping(v_e____,X0,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0)) ),
inference(superposition,[status(thm)],[c_1183,c_1172]) ).
tcf(c_2350,plain,
( ~ c_Type_Otyping(v_e____,v_u____,v_T____)
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
inference(superposition,[status(thm)],[c_1462,c_1184]) ).
tcf(c_2351,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2350,c_1181,c_1182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL836-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 00:34:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 4.85/1.35 % SZS status Started for theBenchmark.p
% 4.85/1.35 % SZS status Unsatisfiable for theBenchmark.p
% 4.85/1.35
% 4.85/1.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.85/1.35
% 4.85/1.35 % ------ iProver source info
% 4.85/1.35
% 4.85/1.35 % git: date: 2026-07-19 20:42:38 +0200
% 4.85/1.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.85/1.35 % git: non_committed_changes: false
% 4.85/1.35
% 4.85/1.35 % ------ Parsing...% successful
% 4.85/1.35
% 4.85/1.35
% 4.85/1.35 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.85/1.35 % ------ Proving...
% 4.85/1.35 % ------ Problem Properties
% 4.85/1.35
% 4.85/1.35 %
% 4.85/1.35 % clauses 542
% 4.85/1.35 % conjectures 1
% 4.85/1.35 % EPR 86
% 4.85/1.35 % Horn 490
% 4.85/1.35 % unary 169
% 4.85/1.35 % binary 198
% 4.85/1.35 % lits 1170
% 4.85/1.35 % lits eq 328
% 4.85/1.35 % fd_pure 0
% 4.85/1.35 % fd_pseudo 0
% 4.85/1.35 % fd_cond 13
% 4.85/1.35 % fd_pseudo_cond 77
% 4.85/1.35 % AC symbols 0
% 4.85/1.35
% 4.85/1.35 % ------ Input Options Time Limit: Unbounded
% 4.85/1.35
% 4.85/1.35
% 4.85/1.35 % ------
% 4.85/1.35 % Current options:
% 4.85/1.35 % ------
% 4.85/1.35
% 4.85/1.35
% 4.85/1.35 %
% 4.85/1.35
% 4.85/1.35 % ------ Proving...
% 4.85/1.35 %
% 4.85/1.35
% 4.85/1.35 % SZS status Unsatisfiable for theBenchmark.p
% 4.85/1.35
% 4.85/1.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.85/1.35
% 4.85/1.35
%------------------------------------------------------------------------------