%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL794-1 : 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 : n011.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 02:08:24 PM UTC 2026
% Result : Unsatisfiable 6.97s 1.63s
% Output : CNFRefutation 6.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 29 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 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 : 16 ( 16 usr; 10 con; 0-5 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f482,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
fof(f484,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/sandbox/benchmark/theBenchmark.p',cls_T_0) ).
fof(f485,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Type_Otyping(X0,X3,X4)
| c_Type_Otyping(c_Type_Oshift(X0,X1,X2,tc_Type_Otype),c_Lambda_Olift(X3,X1),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
fof(f489,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/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
fof(f494,axiom,
! [X2,X3,X0,X1] : hAPP(c_Type_Oshift(X0,X1,X2,X3),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
fof(f497,axiom,
! [X0,X1] : c_Type_Otyping(X0,c_Lambda_OdB_OVar(X1),hAPP(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
fof(f499,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),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_conjecture_0) ).
tcf(c_819,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(cnf_transformation,[],[f482]) ).
tcf(c_821,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,[],[f484]) ).
tcf(c_822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Type_Otyping(c_Type_Oshift(X0,X3,X4,tc_Type_Otype),c_Lambda_Olift(X1,X3),X2)
| ~ c_Type_Otyping(X0,X1,X2) ),
inference(cnf_transformation,[],[f485]) ).
tcf(c_826,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,[],[f489]) ).
tcf(c_831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : hAPP(c_Type_Oshift(X0,X1,X2,X3),X1) = X2,
inference(cnf_transformation,[],[f494]) ).
tcf(c_834,plain,
! [X0: $i,X1: $i] : c_Type_Otyping(X0,c_Lambda_OdB_OVar(X1),hAPP(X0,X1)),
inference(cnf_transformation,[],[f497]) ).
tcf(c_836,negated_conjecture,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat))),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,[],[f499]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : c_Type_Otyping(c_Type_Oshift(X0,X1,X2,X3),c_Lambda_OdB_OVar(X1),X2),
inference(superposition,[status(thm)],[c_831,c_834]) ).
tcf(c_1141,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_821,c_826]) ).
tcf(c_1638,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),v_T_H_H____)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),v_T____) ),
inference(superposition,[status(thm)],[c_1141,c_836]) ).
tcf(c_4817,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,c_HOL_Ozero__class_Ozero(tc_nat),v_T_H_H____,tc_Type_Otype),c_Lambda_Olift(v_u____,c_HOL_Ozero__class_Ozero(tc_nat)),v_T____),
inference(forward_subsumption_resolution,[status(thm)],[c_1638,c_964]) ).
tcf(c_4818,plain,
~ c_Type_Otyping(v_e____,v_u____,v_T____),
inference(superposition,[status(thm)],[c_822,c_4817]) ).
tcf(c_4819,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_819,c_4818]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL794-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.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 00:30:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.42 % Proving...
% 6.97/1.63 % SZS status Started for theBenchmark.p
% 6.97/1.63 % SZS status Unsatisfiable for theBenchmark.p
% 6.97/1.63
% 6.97/1.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.97/1.63
% 6.97/1.63 % ------ iProver source info
% 6.97/1.63
% 6.97/1.63 % git: date: 2026-07-19 20:42:38 +0200
% 6.97/1.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.97/1.63 % git: non_committed_changes: false
% 6.97/1.63
% 6.97/1.63 % ------ Parsing...% successful
% 6.97/1.63
% 6.97/1.63
% 6.97/1.63 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 6.97/1.63 % ------ Proving...
% 6.97/1.63 % ------ Problem Properties
% 6.97/1.63
% 6.97/1.63 %
% 6.97/1.63 % clauses 378
% 6.97/1.63 % conjectures 1
% 6.97/1.63 % EPR 43
% 6.97/1.63 % Horn 344
% 6.97/1.63 % unary 151
% 6.97/1.63 % binary 151
% 6.97/1.63 % lits 711
% 6.97/1.63 % lits eq 305
% 6.97/1.63 % fd_pure 0
% 6.97/1.63 % fd_pseudo 0
% 6.97/1.63 % fd_cond 21
% 6.97/1.63 % fd_pseudo_cond 58
% 6.97/1.63 % AC symbols 0
% 6.97/1.63
% 6.97/1.63 % ------ Input Options Time Limit: Unbounded
% 6.97/1.63
% 6.97/1.63
% 6.97/1.63 % ------
% 6.97/1.63 % Current options:
% 6.97/1.63 % ------
% 6.97/1.63
% 6.97/1.63
% 6.97/1.63 %
% 6.97/1.63
% 6.97/1.63 % ------ Proving...
% 6.97/1.63 %
% 6.97/1.63
% 6.97/1.63 % SZS status Unsatisfiable for theBenchmark.p
% 6.97/1.63
% 6.97/1.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.97/1.63
% 6.97/1.63
%------------------------------------------------------------------------------