%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL847-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Thu Sep 24 01:08:58 PM UTC 2026
% Result : Unsatisfiable 146.37s 19.25s
% Output : CNFRefutation 135.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 59 ( 31 unt; 0 def)
% Number of atoms : 88 ( 52 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 30 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-4 aty)
% Number of variables : 175 ( 175 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f259,axiom,
! [V_x,V_y,V_n,T_a] :
( ~ c_in(V_x,c_List_Oset(c_List_Oreplicate(V_n,V_y,T_a),T_a),T_a)
| V_x = V_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f297,axiom,
! [V_A,V_xs,T_a] :
( c_in(c_List_Osko__List__Xin__listsp__conv__set__1__1(V_A,V_xs,T_a),c_List_Oset(V_xs,T_a),T_a)
| c_List_Olistsp(V_A,V_xs,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f310,axiom,
! [V_xs,V_i,V_x,T_a] : c_Nat_Osize__class_Osize(c_List_Olist__update(V_xs,V_i,V_x,T_a),tc_List_Olist(T_a)) = c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f339,axiom,
! [V_x,V_xa,T_a,V_zs] : c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a) = c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f341,axiom,
! [V_f,V_x,V_xa,T_b,T_a] : c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a) = c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f351,axiom,
! [V_xs,V_x,T_a] : c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a) = V_xs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f355,axiom,
! [V_i,V_x,T_a] : c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f378,axiom,
! [V_ys,T_a] : V_ys = c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f420,axiom,
! [V_f,V_n,V_x,T_b,T_a] : c_List_Omap(V_f,c_List_Oreplicate(V_n,V_x,T_b),T_b,T_a) = c_List_Oreplicate(V_n,hAPP(V_f,V_x),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f518,axiom,
! [V_A,V_xs,T_a] :
( ~ hBOOL(hAPP(V_A,c_List_Osko__List__Xin__listsp__conv__set__1__1(V_A,V_xs,T_a)))
| c_List_Olistsp(V_A,V_xs,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f521,axiom,
! [V_A,V_xs,T_a,V_ys] :
( ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a)
| c_List_Olistsp(V_A,V_xs,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f538,axiom,
! [V_x,V_xs,T_a,V_y] : c_List_Olist__update(c_List_Olist_OCons(V_x,V_xs,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a) = c_List_Olist_OCons(V_y,V_xs,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f541,axiom,
! [V_xs,T_a] :
( V_xs = c_List_Olist_ONil(T_a)
| c_Nat_Osize__class_Osize(V_xs,tc_List_Olist(T_a)) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f542,axiom,
! [T_a,V_n,V_x] :
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Olist_ONil(T_a) != c_List_Oreplicate(V_n,V_x,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f554,axiom,
! [V_x,V_xs,T_a] :
( V_xs = c_List_Olist_ONil(T_a)
| c_List_Obutlast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Obutlast(V_xs,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f578,axiom,
! [T_a,V_a_H,V_list_H] : c_List_Olist_ONil(T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f586,axiom,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f587,negated_conjecture,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1041,plain,
! [V_x,V_y] :
( ! [V_n,T_a] : ~ c_in(V_x,c_List_Oset(c_List_Oreplicate(V_n,V_y,T_a),T_a),T_a)
| V_x = V_y ),
inference(miniscoping,[status(thm)],[f259]) ).
fof(f1042,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X0,c_List_Oset(c_List_Oreplicate(X2,X1,X3),X3),X3)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f1041]) ).
fof(f1104,plain,
! [X0,X1,X2] :
( c_in(c_List_Osko__List__Xin__listsp__conv__set__1__1(X0,X1,X2),c_List_Oset(X1,X2),X2)
| c_List_Olistsp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f1121,plain,
! [X0,X1,X2,X3] : c_Nat_Osize__class_Osize(c_List_Olist__update(X0,X1,X2,X3),tc_List_Olist(X3)) = c_Nat_Osize__class_Osize(X0,tc_List_Olist(X3)),
inference(cnf_transformation,[status(thm)],[f310]) ).
fof(f1169,plain,
! [X0,X1,X2,X3] : c_List_Oappend(c_List_Olist_OCons(X0,X1,X2),X3,X2) = c_List_Olist_OCons(X0,c_List_Oappend(X1,X3,X2),X2),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f1171,plain,
! [X0,X1,X2,X3,X4] : c_List_Omap(X0,c_List_Olist_OCons(X1,X2,X3),X3,X4) = c_List_Olist_OCons(hAPP(X0,X1),c_List_Omap(X0,X2,X3,X4),X4),
inference(cnf_transformation,[status(thm)],[f341]) ).
fof(f1183,plain,
! [X0,X1,X2] : c_List_Obutlast(c_List_Oappend(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2),X2) = X0,
inference(cnf_transformation,[status(thm)],[f351]) ).
fof(f1187,plain,
! [X0,X1,X2] : c_List_Oappend(c_List_Oreplicate(X0,X1,X2),c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) = c_List_Olist_OCons(X1,c_List_Oreplicate(X0,X1,X2),X2),
inference(cnf_transformation,[status(thm)],[f355]) ).
fof(f1221,plain,
! [X0,X1] : X0 = c_List_Oappend(c_List_Olist_ONil(X1),X0,X1),
inference(cnf_transformation,[status(thm)],[f378]) ).
fof(f1279,plain,
! [X0,X1,X2,X3,X4] : c_List_Omap(X0,c_List_Oreplicate(X1,X2,X3),X3,X4) = c_List_Oreplicate(X1,hAPP(X0,X2),X4),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f1417,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X0,c_List_Osko__List__Xin__listsp__conv__set__1__1(X0,X1,X2)))
| c_List_Olistsp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f518]) ).
fof(f1422,plain,
! [V_A,V_xs,T_a] :
( ! [V_ys] : ~ c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a)
| c_List_Olistsp(V_A,V_xs,T_a) ),
inference(miniscoping,[status(thm)],[f521]) ).
fof(f1423,plain,
! [X0,X1,X2,X3] :
( ~ c_List_Olistsp(X0,c_List_Oappend(X1,X3,X2),X2)
| c_List_Olistsp(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1422]) ).
fof(f1449,plain,
! [X0,X1,X2,X3] : c_List_Olist__update(c_List_Olist_OCons(X0,X1,X2),c_HOL_Ozero__class_Ozero(tc_nat),X3,X2) = c_List_Olist_OCons(X3,X1,X2),
inference(cnf_transformation,[status(thm)],[f538]) ).
fof(f1452,plain,
! [X0,X1] :
( X0 = c_List_Olist_ONil(X1)
| c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(cnf_transformation,[status(thm)],[f541]) ).
fof(f1453,plain,
! [V_n] :
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| ! [T_a,V_x] : c_List_Olist_ONil(T_a) != c_List_Oreplicate(V_n,V_x,T_a) ),
inference(miniscoping,[status(thm)],[f542]) ).
fof(f1454,plain,
! [X0,X1,X2] :
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X1,X2,X0) ),
inference(cnf_transformation,[status(thm)],[f1453]) ).
fof(f1471,plain,
! [V_xs,T_a] :
( V_xs = c_List_Olist_ONil(T_a)
| ! [V_x] : c_List_Obutlast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_List_Olist_OCons(V_x,c_List_Obutlast(V_xs,T_a),T_a) ),
inference(miniscoping,[status(thm)],[f554]) ).
fof(f1472,plain,
! [X0,X1,X2] :
( X1 = c_List_Olist_ONil(X2)
| c_List_Obutlast(c_List_Olist_OCons(X0,X1,X2),X2) = c_List_Olist_OCons(X0,c_List_Obutlast(X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f1471]) ).
fof(f1507,plain,
! [X0,X1,X2] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X1,X2,X0),
inference(cnf_transformation,[status(thm)],[f578]) ).
fof(f1516,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)))),
inference(cnf_transformation,[status(thm)],[f586]) ).
fof(f1517,plain,
~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
inference(cnf_transformation,[status(thm)],[f587]) ).
fof(f7200,plain,
! [X0,X1,X2,X3] :
( c_List_Osko__List__Xin__listsp__conv__set__1__1(X0,c_List_Oreplicate(X1,X2,X3),X3) = X2
| c_List_Olistsp(X0,c_List_Oreplicate(X1,X2,X3),X3) ),
inference(resolution,[status(thm)],[f1104,f1042]) ).
fof(f7220,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__update(X0,X2,X3,X1) = c_List_Olist_ONil(X1)
| c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1121,f1452]) ).
fof(f14693,plain,
! [X0,X1,X2] : c_List_Oappend(c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1),X2,X1) = c_List_Olist_OCons(X0,X2,X1),
inference(paramodulation,[status(thm)],[f1221,f1169]) ).
fof(f14763,plain,
! [X0,X1,X2,X3] :
( ~ c_List_Olistsp(X0,c_List_Olist_OCons(X1,X3,X2),X2)
| c_List_Olistsp(X0,c_List_Olist_OCons(X1,c_List_Olist_ONil(X2),X2),X2) ),
inference(paramodulation,[status(thm)],[f14693,f1423]) ).
fof(f15801,plain,
! [X0,X1,X2,X3] :
( c_List_Olist_OCons(X3,X1,X2) = c_List_Olist_ONil(X2)
| c_Nat_Osize__class_Osize(c_List_Olist_OCons(X0,X1,X2),tc_List_Olist(X2)) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1449,f7220]) ).
fof(f15809,plain,
! [X0,X1,X2] : c_Nat_Osize__class_Osize(c_List_Olist_OCons(X0,X1,X2),tc_List_Olist(X2)) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(forward_subsumption_resolution,[status(thm)],[f15801,f1507]) ).
fof(f15812,plain,
! [X0,X1,X2,X3] : c_Nat_Osize__class_Osize(c_List_Oappend(c_List_Olist_OCons(X0,X1,X2),X3,X2),tc_List_Olist(X2)) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(paramodulation,[status(thm)],[f1169,f15809]) ).
fof(f16037,plain,
! [X0] : ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_Lambda_OdB),tc_Lambda_OdB),
inference(resolution,[status(thm)],[f14763,f1517]) ).
fof(f39559,plain,
! [X0,X1,X2,X3] :
( c_List_Olistsp(X0,c_List_Oreplicate(X1,X2,X3),X3)
| ~ hBOOL(hAPP(X0,X2))
| c_List_Olistsp(X0,c_List_Oreplicate(X1,X2,X3),X3) ),
inference(paramodulation,[status(thm)],[f7200,f1417]) ).
fof(f39565,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(X0,X2))
| c_List_Olistsp(X0,c_List_Oreplicate(X1,X2,X3),X3) ),
inference(duplicate_literals_removal,[status(thm)],[f39559]) ).
fof(f66641,plain,
! [X0,X1] : ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_Lambda_Olift,v_ta____),c_List_Olist_OCons(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1),X1,tc_Lambda_OdB),tc_Lambda_OdB),
inference(paramodulation,[status(thm)],[f1171,f16037]) ).
fof(f70688,plain,
! [X0,X1,X2] : c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Oreplicate(X1,X0,X2),X2),X2) = c_List_Oreplicate(X1,X0,X2),
inference(paramodulation,[status(thm)],[f1187,f1183]) ).
fof(f77504,plain,
! [X0,X1] :
( X0 = c_List_Olist_ONil(X1)
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_Lambda_Olift,v_ta____),c_List_Obutlast(c_List_Olist_OCons(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1),X1),X1,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(paramodulation,[status(thm)],[f1472,f66641]) ).
fof(f78266,plain,
! [X0,X1] :
( c_List_Oreplicate(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_List_Olist_ONil(X1)
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(c_Lambda_Olift,v_ta____),c_List_Oreplicate(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1,tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(paramodulation,[status(thm)],[f70688,f77504]) ).
fof(f78271,plain,
! [X0,X1] :
( c_List_Oreplicate(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_List_Olist_ONil(X1)
| ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Oreplicate(X0,hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),tc_Lambda_OdB),tc_Lambda_OdB) ),
inference(forward_demodulation,[status(thm)],[f1279,f78266]) ).
fof(f78279,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat))))
| c_List_Oreplicate(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_List_Olist_ONil(X1) ),
inference(resolution,[status(thm)],[f78271,f39565]) ).
fof(f78289,plain,
! [X0,X1] : c_List_Oreplicate(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1) = c_List_Olist_ONil(X1),
inference(forward_subsumption_resolution,[status(thm)],[f78279,f1516]) ).
fof(f78293,plain,
! [X0] : X0 = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolution,[status(thm)],[f78289,f1454]) ).
fof(f78615,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f15812,f78293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL847-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 01:03:43 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.42 % Drodi V4.1.1
% 146.37/19.25 % Refutation found
% 146.37/19.25 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 146.37/19.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 42.26/19.40 % Elapsed time: 18.986774 seconds
% 42.26/19.40 % CPU time: 149.763545 seconds
% 42.26/19.40 % Total memory used: 741.557 MB
% 42.26/19.40 % Net memory used: 679.222 MB
%------------------------------------------------------------------------------