%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL795-1 : 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 : 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 02:08:24 PM UTC 2026
% Result : Unsatisfiable 3.50s 1.09s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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; 8 con; 0-5 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1006,axiom,
! [X2,X3,X0,X1,X4,X5] : c_List_Ofoldr(X0,c_List_Olist_OCons(X1,X2,X3),X4,X3,X5) = hAPP(hAPP(X0,X1),c_List_Ofoldr(X0,X2,X4,X3,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
fof(f1037,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(f1040,axiom,
c_Type_Otyping(v_e____,v_u____,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_uT_H_0) ).
fof(f1042,negated_conjecture,
~ 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)),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_conjecture_0) ).
tcf(c_1655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : hAPP(hAPP(X0,X1),c_List_Ofoldr(X0,X2,X3,X4,X5)) = c_List_Ofoldr(X0,c_List_Olist_OCons(X1,X2,X4),X3,X4,X5),
inference(cnf_transformation,[],[f1006]) ).
tcf(c_1682,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,[],[f1037]) ).
tcf(c_1685,plain,
c_Type_Otyping(v_e____,v_u____,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))),
inference(cnf_transformation,[],[f1040]) ).
tcf(c_1687,negated_conjecture,
~ 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)),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))),
inference(cnf_transformation,[],[f1042]) ).
tcf(c_1889,plain,
c_Type_Otyping(v_e____,v_u____,c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(superposition,[status(thm)],[c_1655,c_1685]) ).
tcf(c_1899,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)),c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(demodulation,[status(thm)],[c_1687,c_1655]) ).
tcf(c_1900,plain,
~ c_Type_Otyping(v_e____,v_u____,c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)),
inference(superposition,[status(thm)],[c_1682,c_1899]) ).
tcf(c_1901,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1900,c_1889]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL795-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n019.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 00:30:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 3.50/1.09 % SZS status Started for theBenchmark.p
% 3.50/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 3.50/1.09
% 3.50/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.50/1.09
% 3.50/1.09 % ------ iProver source info
% 3.50/1.09
% 3.50/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 3.50/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.50/1.09 % git: non_committed_changes: false
% 3.50/1.09
% 3.50/1.09 % ------ Parsing...% successful
% 3.50/1.09
% 3.50/1.09
% 3.50/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.50/1.09 % ------ Proving...
% 3.50/1.09 % ------ Problem Properties
% 3.50/1.09
% 3.50/1.09 %
% 3.50/1.09 % clauses 759
% 3.50/1.09 % conjectures 1
% 3.50/1.09 % EPR 98
% 3.50/1.09 % Horn 684
% 3.50/1.09 % unary 205
% 3.50/1.09 % binary 279
% 3.50/1.09 % lits 1726
% 3.50/1.09 % lits eq 465
% 3.50/1.09 % fd_pure 0
% 3.50/1.09 % fd_pseudo 0
% 3.50/1.09 % fd_cond 22
% 3.50/1.09 % fd_pseudo_cond 91
% 3.50/1.09 % AC symbols 0
% 3.50/1.09
% 3.50/1.09 % ------ Input Options Time Limit: Unbounded
% 3.50/1.09
% 3.50/1.09
% 3.50/1.09 % ------
% 3.50/1.09 % Current options:
% 3.50/1.09 % ------
% 3.50/1.09
% 3.50/1.09
% 3.50/1.09 %
% 3.50/1.09
% 3.50/1.09 % ------ Proving...
% 3.50/1.09 %
% 3.50/1.09
% 3.50/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 3.50/1.09
% 3.50/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.50/1.09
% 3.50/1.09
%------------------------------------------------------------------------------