%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL787-1 : 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 : n015.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 02:08:23 PM UTC 2026
% Result : Unsatisfiable 37.37s 10.19s
% Output : CNFRefutation 37.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 34 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 20 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-5 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f282,axiom,
! [X2,X3,X0,X1] :
( ~ c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X3),X1),X2)
| c_Type_Otyping(X0,X1,c_Type_Osko__Type__Xtyping__elims__2__1(X2,X0,X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
fof(f430,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
fof(f450,axiom,
! [X0] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,X0),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
fof(f457,axiom,
! [X2,X3,X0,X1] :
( ~ c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X3),X2)
| c_Type_Otyping(X0,X1,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X2,X0,X1,X3)),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
fof(f459,axiom,
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,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f460,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f486,plain,
! [X0] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,X0),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
| v_thesis____ ),
inference(definition_unfolding,[],[f450,f430]) ).
fof(f487,plain,
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_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(definition_unfolding,[],[f459,f430]) ).
tcf(c_632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Type_Otyping(X0,X2,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X0,X1,X2))
| ~ c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_757,plain,
! [X0: $i] :
( v_thesis____
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,X0),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(cnf_transformation,[],[f486]) ).
tcf(c_764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Type_Otyping(X0,X1,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X3,X0,X1,X2)),X3))
| ~ c_Type_Otyping(X0,hAPP(hAPP(c_Lambda_OdB_OApp,X1),X2),X3) ),
inference(cnf_transformation,[],[f457]) ).
tcf(c_766,plain,
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_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(cnf_transformation,[],[f487]) ).
tcf(c_767,negated_conjecture,
~ v_thesis____,
inference(cnf_transformation,[],[f460]) ).
tcf(c_1029,plain,
! [X0: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,X0),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0) ),
inference(global_subsumption_just,[status(thm)],[c_757,c_767,c_757]) ).
tcf(c_1030,plain,
! [X0: $i] :
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,X0)
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,X0),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(renaming,[status(thm)],[c_1029]) ).
tcf(c_2345,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_a____))
| ~ 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_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
inference(instantiation,[status(thm)],[c_632]) ).
tcf(c_2512,plain,
( c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))
| ~ 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_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
inference(instantiation,[status(thm)],[c_764]) ).
tcf(c_3749,plain,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_a____))
| ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
inference(instantiation,[status(thm)],[c_1030]) ).
tcf(c_3750,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3749,c_2512,c_2345,c_766]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL787-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.45 % Computer : n015.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 00:32:57 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.24/0.50 Running first-order theorem proving
% 0.24/0.50 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
% 0.24/0.52
% 0.24/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.52
% 0.24/0.52 % Detected problem language: tptp
% 0.24/0.53 % Proving...
% 37.37/10.19 % SZS status Started for theBenchmark.p
% 37.37/10.19 % SZS status Unsatisfiable for theBenchmark.p
% 37.37/10.19
% 37.37/10.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 37.37/10.19
% 37.37/10.19 % ------ iProver source info
% 37.37/10.19
% 37.37/10.19 % git: date: 2026-07-19 20:42:38 +0200
% 37.37/10.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 37.37/10.19 % git: non_committed_changes: false
% 37.37/10.19
% 37.37/10.19 % ------ Parsing...% successful
% 37.37/10.19
% 37.37/10.19
% 37.37/10.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 37.37/10.19
% 37.37/10.19 % ------ Preprocessing... sf_s rm: 2 0s sf_e sf_s rm: 1 0s sf_e %
% 37.37/10.19
% 37.37/10.19 % ------ Preprocessing...%
% 37.37/10.19
% 37.37/10.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 37.37/10.19 % ------ Proving...
% 37.37/10.19 % ------ Problem Properties
% 37.37/10.19
% 37.37/10.19 %
% 37.37/10.19 % clauses 305
% 37.37/10.19 % conjectures 0
% 37.37/10.19 % EPR 31
% 37.37/10.19 % Horn 274
% 37.37/10.19 % unary 110
% 37.37/10.19 % binary 130
% 37.37/10.19 % lits 580
% 37.37/10.19 % lits eq 240
% 37.37/10.19 % fd_pure 0
% 37.37/10.19 % fd_pseudo 0
% 37.37/10.19 % fd_cond 4
% 37.37/10.19 % fd_pseudo_cond 55
% 37.37/10.19 % AC symbols 0
% 37.37/10.19
% 37.37/10.19 % ------ Input Options Time Limit: Unbounded
% 37.37/10.19
% 37.37/10.19
% 37.37/10.19 % ------
% 37.37/10.19 % Current options:
% 37.37/10.19 % ------
% 37.37/10.19
% 37.37/10.19
% 37.37/10.19 %
% 37.37/10.19
% 37.37/10.19 % ------ Proving...
% 37.37/10.19 %
% 37.37/10.19
% 37.37/10.19 % SZS status Unsatisfiable for theBenchmark.p
% 37.37/10.19
% 37.37/10.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 37.37/10.19
% 37.37/10.19
%------------------------------------------------------------------------------