%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL818-1 : 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 : n002.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 02:08:29 PM UTC 2026
% Result : Unsatisfiable 4.30s 1.31s
% Output : CNFRefutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 20 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-5 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f388,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uT_0) ).
fof(f405,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Type_Otyping(X0,X1,hAPP(hAPP(c_Type_Otype_OFun,X4),X3))
| ~ c_Type_Otyping(X0,X2,X4)
| c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_0) ).
fof(f430,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_T_0) ).
fof(f450,axiom,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f452,negated_conjecture,
~ c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tcf(c_745,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(cnf_transformation,[],[f388]) ).
tcf(c_760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X4),X3)
| ~ c_Type_Otyping(X0,X4,X2)
| ~ c_Type_Otyping(X0,X1,hAPP(hAPP(c_Type_Otype_OFun,X2),X3)) ),
inference(cnf_transformation,[],[f405]) ).
tcf(c_784,plain,
hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) = v_T____,
inference(cnf_transformation,[],[f430]) ).
tcf(c_803,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(cnf_transformation,[],[f450]) ).
tcf(c_805,negated_conjecture,
~ c_Type_Otyping(v_e____,hAPP(hAPP(c_Lambda_OdB_OApp,v_u____),c_Lambda_Osubst(v_a____,v_u____,v_i____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(cnf_transformation,[],[f452]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))
| ~ c_Type_Otyping(X0,X2,v_T_H_H____)
| ~ c_Type_Otyping(X0,X1,v_T____) ),
inference(superposition,[status(thm)],[c_784,c_760]) ).
tcf(c_2298,plain,
( ~ c_Type_Otyping(v_e____,v_u____,v_T____)
| ~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____) ),
inference(superposition,[status(thm)],[c_1018,c_805]) ).
tcf(c_2300,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2298,c_803,c_745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL818-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 00:35:03 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 4.30/1.31 % SZS status Started for theBenchmark.p
% 4.30/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.30/1.31
% 4.30/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.30/1.31
% 4.30/1.31 % ------ iProver source info
% 4.30/1.31
% 4.30/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.30/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.30/1.31 % git: non_committed_changes: false
% 4.30/1.31
% 4.30/1.31 % ------ Parsing...% successful
% 4.30/1.31
% 4.30/1.31
% 4.30/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.30/1.31 % ------ Proving...
% 4.30/1.31 % ------ Problem Properties
% 4.30/1.31
% 4.30/1.31 %
% 4.30/1.31 % clauses 382
% 4.30/1.31 % conjectures 1
% 4.30/1.31 % EPR 38
% 4.30/1.31 % Horn 353
% 4.30/1.31 % unary 137
% 4.30/1.31 % binary 175
% 4.30/1.31 % lits 716
% 4.30/1.31 % lits eq 271
% 4.30/1.31 % fd_pure 0
% 4.30/1.31 % fd_pseudo 0
% 4.30/1.31 % fd_cond 10
% 4.30/1.31 % fd_pseudo_cond 58
% 4.30/1.31 % AC symbols 0
% 4.30/1.31
% 4.30/1.31 % ------ Input Options Time Limit: Unbounded
% 4.30/1.31
% 4.30/1.31
% 4.30/1.31 % ------
% 4.30/1.31 % Current options:
% 4.30/1.31 % ------
% 4.30/1.31
% 4.30/1.31
% 4.30/1.31 %
% 4.30/1.31
% 4.30/1.31 % ------ Proving...
% 4.30/1.31 %
% 4.30/1.31
% 4.30/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.30/1.31
% 4.30/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.30/1.31
% 4.30/1.31
%------------------------------------------------------------------------------