%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL788-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 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 : Mon Sep 7 11:12:44 AM UTC 2026
% Result : Unsatisfiable 27.20s 8.00s
% Output : CNFRefutation 27.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 60 ( 60 usr; 22 con; 0-5 aty)
% Number of variables : 26 ( 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_ListOrder_Ostep1 > c_fequal > c_Type_Otypings > c_Type_Otyping > c_List_Olistsp > hBOOL > c_List_Osko__List__Xappend__eq__Cons__conv__1__1 > c_List_Osko__List__XCons__eq__append__conv__1__1 > c_List_Ofoldr > c_List_Ofoldl > c_Type_Otype_Otype__rec > c_Type_Otype_Otype__case > c_Type_Osko__Type__Xvar__app__types__1__1 > c_Type_Osko__Type__Xvar__app__typesE__1__1 > c_Type_Osko__Type__Xtyping__elims__2__1 > c_Type_Osko__Type__Xtypes__snocE__1__2 > c_Type_Osko__Type__Xlist__app__typeE__1__1 > c_Type_Osko__Type__Xlist__app__typeD__1__1 > c_Type_Oshift > c_List_Oconcat__map > c_COMBC > c_List_OtakeWhile > c_List_Osplice > c_List_Osko__List__Xsplit__list__last__prop__iff__1__5 > c_List_Osko__List__Xsplit__list__first__prop__iff__1__5 > c_List_Oreplicate > c_List_Olist_OCons > c_List_OdropWhile > c_List_Oappend > c_Lambda_Osubst > hAPP > c_List_Otl > c_List_Orotate1 > c_List_Orev > c_List_Olast > c_List_Ohd > c_List_Obutlast > c_Lambda_Olift > #nlpp > c_Type_Otype_OAtom > c_Type_Osko__Type__Xtype__induct__1__1 > c_List_Olist_ONil > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > v_ua______ > v_u____ > v_rs____ > v_n____ > v_ia______ > v_i____ > v_ea______ > v_e____ > v_as____ > v_a____ > v_Ts____ > v_T____ > v_T_Ha______ > v_T_H____ > v_T_H_H____ > tc_nat > tc_Type_Otype > tc_Lambda_OdB > t_a > c_Type_Otype_OFun > c_Lambda_OdB_OApp > c_InductTermi_OIT
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_Lambda_Olift,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(c_List_Osko__List__Xsplit__list__first__prop__iff__1__5,type,
c_List_Osko__List__Xsplit__list__first__prop__iff__1__5: ( $i * $i * $i ) > $i ).
tff(c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
tff(c_Type_Osko__Type__Xtype__induct__1__1,type,
c_Type_Osko__Type__Xtype__induct__1__1: $i > $i ).
tff(c_List_Oappend,type,
c_List_Oappend: ( $i * $i * $i ) > $i ).
tff(tc_Type_Otype,type,
tc_Type_Otype: $i ).
tff(c_Type_Osko__Type__Xvar__app__typesE__1__1,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Oconcat__map,type,
c_List_Oconcat__map: ( $i * $i * $i * $i ) > $i ).
tff(c_List_OdropWhile,type,
c_List_OdropWhile: ( $i * $i * $i ) > $i ).
tff(c_List_Orev,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(v_T_Ha______,type,
v_T_Ha______: $i ).
tff(c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
tff(c_List_Obutlast,type,
c_List_Obutlast: ( $i * $i ) > $i ).
tff(t_a,type,
t_a: $i ).
tff(c_List_OtakeWhile,type,
c_List_OtakeWhile: ( $i * $i * $i ) > $i ).
tff(c_List_Ofoldl,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_List_Olistsp,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(c_Type_Osko__Type__Xlist__app__typeD__1__1,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Lambda_Osubst,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(v_rs____,type,
v_rs____: $i ).
tff(v_ia______,type,
v_ia______: $i ).
tff(c_Type_Osko__Type__Xvar__app__types__1__1,type,
c_Type_Osko__Type__Xvar__app__types__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Type_Otype_OAtom,type,
c_Type_Otype_OAtom: $i > $i ).
tff(c_List_Otl,type,
c_List_Otl: ( $i * $i ) > $i ).
tff(c_ListOrder_Ostep1,type,
c_ListOrder_Ostep1: ( $i * $i * $i * $i ) > $o ).
tff(c_List_Oreplicate,type,
c_List_Oreplicate: ( $i * $i * $i ) > $i ).
tff(c_Type_Osko__Type__Xtyping__elims__2__1,type,
c_Type_Osko__Type__Xtyping__elims__2__1: ( $i * $i * $i * $i ) > $i ).
tff(v_ea______,type,
v_ea______: $i ).
tff(c_List_Ofoldr,type,
c_List_Ofoldr: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_ua______,type,
v_ua______: $i ).
tff(c_Type_Osko__Type__Xtypes__snocE__1__2,type,
c_Type_Osko__Type__Xtypes__snocE__1__2: ( $i * $i * $i * $i ) > $i ).
tff(c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(c_Type_Oshift,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(v_n____,type,
v_n____: $i ).
tff(c_Type_Otyping,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(v_e____,type,
v_e____: $i ).
tff(c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(c_Type_Osko__Type__Xlist__app__typeE__1__1,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i ).
tff(c_List_Osko__List__XCons__eq__append__conv__1__1,type,
c_List_Osko__List__XCons__eq__append__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Type_Otypings,type,
c_Type_Otypings: ( $i * $i * $i ) > $o ).
tff(c_List_Osplice,type,
c_List_Osplice: ( $i * $i * $i ) > $i ).
tff(tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_fequal,type,
c_fequal: ( $i * $i * $i ) > $o ).
tff(c_Type_Otype_Otype__rec,type,
c_Type_Otype_Otype__rec: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Osko__List__Xappend__eq__Cons__conv__1__1,type,
c_List_Osko__List__Xappend__eq__Cons__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Type_Otype_Otype__case,type,
c_Type_Otype_Otype__case: ( $i * $i * $i * $i ) > $i ).
tff(v_Ts____,type,
v_Ts____: $i ).
tff(c_Type_Otype_OFun,type,
c_Type_Otype_OFun: $i ).
tff(c_List_Olist_OCons,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(c_List_Ohd,type,
c_List_Ohd: ( $i * $i ) > $i ).
tff(v_T____,type,
v_T____: $i ).
tff(c_List_Orotate1,type,
c_List_Orotate1: ( $i * $i ) > $i ).
tff(v_i____,type,
v_i____: $i ).
tff(v_as____,type,
v_as____: $i ).
tff(v_a____,type,
v_a____: $i ).
tff(v_T_H____,type,
v_T_H____: $i ).
tff(v_u____,type,
v_u____: $i ).
tff(c_List_Osko__List__Xsplit__list__last__prop__iff__1__5,type,
c_List_Osko__List__Xsplit__list__last__prop__iff__1__5: ( $i * $i * $i ) > $i ).
tff(v_T_H_H____,type,
v_T_H_H____: $i ).
tff(c_List_Olast,type,
c_List_Olast: ( $i * $i ) > $i ).
tff(c_COMBC,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(f_925,axiom,
! [V_a,T_a,V_f,V_xs,T_b,V_x] : ( c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a) = hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)) ),
file(unknown,unknown) ).
tff(f_966,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(unknown,unknown) ).
tff(f_806,axiom,
! [V_e,V_x,V_T,T_a] : ( hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x) = V_T ),
file(unknown,unknown) ).
tff(f_963,axiom,
v_n____ = v_i____,
file(unknown,unknown) ).
tff(f_964,axiom,
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,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file(unknown,unknown) ).
tff(f_803,axiom,
! [V_e,V_i,V_T] :
( ( hAPP(V_e,V_i) = V_T )
| ~ c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T) ),
file(unknown,unknown) ).
tff(c_452,plain,
! [V_xs_748,T_b_749,V_a_745,T_a_746,V_f_747,V_x_750] : ( hAPP(hAPP(V_f_747,V_x_750),c_List_Ofoldr(V_f_747,V_xs_748,V_a_745,T_b_749,T_a_746)) = c_List_Ofoldr(V_f_747,c_List_Olist_OCons(V_x_750,V_xs_748,T_b_749),V_a_745,T_b_749,T_a_746) ),
inference(cnfTransformation,[status(thm)],[f_925]) ).
tff(c_480,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(cnfTransformation,[status(thm)],[f_966]) ).
tff(c_490,plain,
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) != v_T____,
inference(demodulation,[status(thm),theory(equality)],[c_452,c_480]) ).
tff(c_392,plain,
! [V_e_641,V_x_642,V_T_643,T_a_644] : ( hAPP(c_Type_Oshift(V_e_641,V_x_642,V_T_643,T_a_644),V_x_642) = V_T_643 ),
inference(cnfTransformation,[status(thm)],[f_806]) ).
tff(c_476,plain,
v_n____ = v_i____,
inference(cnfTransformation,[status(thm)],[f_963]) ).
tff(c_478,plain,
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,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(cnfTransformation,[status(thm)],[f_964]) ).
tff(c_485,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,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(demodulation,[status(thm),theory(equality)],[c_476,c_478]) ).
tff(c_489,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),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),theory(equality)],[c_452,c_485]) ).
tff(c_388,plain,
! [V_e_638,V_i_639,V_T_640] :
( ~ c_Type_Otyping(V_e_638,c_Lambda_OdB_OVar(V_i_639),V_T_640)
| ( hAPP(V_e_638,V_i_639) = V_T_640 ) ),
inference(cnfTransformation,[status(thm)],[f_803]) ).
tff(c_8055,plain,
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) = hAPP(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_i____),
inference(resolution,[status(thm)],[c_489,c_388]) ).
tff(c_8057,plain,
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) = v_T____,
inference(demodulation,[status(thm),theory(equality)],[c_392,c_8055]) ).
tff(c_8059,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_490,c_8057]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL788-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.41 % Computer : n015.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 6 00:21:58 UTC 2026
% 0.15/0.41 % CPUTime :
% 27.20/8.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.20/8.01
% 27.20/8.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------