%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV751-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 : Thu Sep 24 02:49:28 PM UTC 2026
% Result : Unsatisfiable 36.09s 5.11s
% Output : CNFRefutation 36.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 24 unt; 0 def)
% Number of atoms : 88 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 34 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 154 ( 154 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_List_Oset(c_List_Olist_ONil(T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [T_a,V_x] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,axiom,
! [V_P,V_keymode] :
( ~ hBOOL(hAPP(V_P,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(V_P,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(V_P,V_keymode)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [V_B,V_a,T_a] : c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f231,axiom,
! [V_x,V_B,T_a,V_A] :
( ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_B,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f393,axiom,
! [V_a,V_A,T_a] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| c_Set_Oinsert(V_a,V_A,T_a) = V_A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f410,axiom,
! [V_xs,V_x,T_a] : V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f413,axiom,
! [V_a_H,V_list_H,T_a] : c_List_Olist_OCons(V_a_H,V_list_H,T_a) != c_List_Olist_ONil(T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f441,axiom,
! [V_A,V_x,V_y,T_a] :
( ~ hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x))
| V_y = V_x
| hBOOL(hAPP(V_A,V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f456,axiom,
! [V_x,V_A,T_a] : hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f463,axiom,
! [V_a,V_list,T_a,V_a_H,V_list_H] :
( V_list = V_list_H
| c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f558,axiom,
! [V_x,V_S,T_a] :
( ~ hBOOL(hAPP(V_S,V_x))
| hBOOL(c_in(V_x,V_S,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f559,axiom,
! [V_S,V_x,T_a] :
( ~ hBOOL(c_in(V_x,V_S,T_a))
| hBOOL(hAPP(V_S,V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f618,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_List_Oset(c_List_Olist_ONil(X0),X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f646,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f694,plain,
! [V_P] :
( ~ hBOOL(hAPP(V_P,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(V_P,c_Public_Okeymode_OEncryption))
| ! [V_keymode] : hBOOL(hAPP(V_P,V_keymode)) ),
inference(miniscoping,[status(thm)],[f70]) ).
fof(f695,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(X0,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(X0,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f694]) ).
fof(f700,plain,
! [X0,X1,X2] : c_lessequals(X0,c_Set_Oinsert(X1,X0,X2),tc_fun(X2,tc_bool)),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f929,plain,
! [V_x,V_B,T_a] :
( ! [V_A] : ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_B,T_a)) ),
inference(miniscoping,[status(thm)],[f231]) ).
fof(f930,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(c_Set_Oinsert(X0,X3,X2),X1,tc_fun(X2,tc_bool))
| hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f929]) ).
fof(f1150,plain,
! [X0,X1,X2] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Set_Oinsert(X0,X1,X2) = X1 ),
inference(cnf_transformation,[status(thm)],[f393]) ).
fof(f1171,plain,
! [X0,X1,X2] : X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f1174,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(thm)],[f413]) ).
fof(f1209,plain,
! [V_A,V_x,V_y] :
( ! [T_a] : ~ hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x))
| V_y = V_x
| hBOOL(hAPP(V_A,V_x)) ),
inference(miniscoping,[status(thm)],[f441]) ).
fof(f1210,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(c_Set_Oinsert(X2,X0,X3),X1))
| X2 = X1
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1209]) ).
fof(f1227,plain,
! [X0,X1,X2] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X0)),
inference(cnf_transformation,[status(thm)],[f456]) ).
fof(f1236,plain,
! [V_list,V_list_H] :
( V_list = V_list_H
| ! [V_a,T_a,V_a_H] : c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a) ),
inference(miniscoping,[status(thm)],[f463]) ).
fof(f1237,plain,
! [X0,X1,X2,X3,X4] :
( X1 = X4
| c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_OCons(X3,X4,X2) ),
inference(cnf_transformation,[status(thm)],[f1236]) ).
fof(f1385,plain,
! [V_x,V_S] :
( ~ hBOOL(hAPP(V_S,V_x))
| ! [T_a] : hBOOL(c_in(V_x,V_S,T_a)) ),
inference(miniscoping,[status(thm)],[f558]) ).
fof(f1386,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f1385]) ).
fof(f1387,plain,
! [V_S,V_x] :
( ! [T_a] : ~ hBOOL(c_in(V_x,V_S,T_a))
| hBOOL(hAPP(V_S,V_x)) ),
inference(miniscoping,[status(thm)],[f559]) ).
fof(f1388,plain,
! [X0,X1,X2] :
( ~ hBOOL(c_in(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1387]) ).
fof(f1815,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_List_Oset(c_List_Olist_ONil(X0),X0),X1)),
inference(paramodulation,[status(thm)],[f618,f646]) ).
fof(f2594,plain,
! [X0,X1,X2,X3] : hBOOL(c_in(X0,c_Set_Oinsert(X0,X1,X2),X3)),
inference(resolution,[status(thm)],[f1227,f1386]) ).
fof(f3096,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,X0,X1),c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,X0,X1),X2)) ),
inference(resolution,[status(thm)],[f695,f1227]) ).
fof(f4774,plain,
! [X0,X1,X2,X3] : c_Set_Oinsert(X0,c_Set_Oinsert(X0,X1,X2),X3) = c_Set_Oinsert(X0,X1,X2),
inference(resolution,[status(thm)],[f1150,f2594]) ).
fof(f13834,plain,
! [X0,X1,X2,X3] : hBOOL(c_in(X0,c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),X3)),
inference(resolution,[status(thm)],[f930,f700]) ).
fof(f21162,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,X2,X3),X3),X1)),
inference(resolution,[status(thm)],[f13834,f1388]) ).
fof(f21342,plain,
! [X0,X1,X2,X3,X4] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,X2,X3),X4),X1)),
inference(paramodulation,[status(thm)],[f4774,f21162]) ).
fof(f54004,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,c_Set_Oinsert(c_Public_Okeymode_OEncryption,X0,X1),X2),X3)),
inference(resolution,[status(thm)],[f3096,f21342]) ).
fof(f54035,plain,
! [X0,X1,X2] :
( c_Public_Okeymode_OSignature = X2
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,X0,X1),X2)) ),
inference(resolution,[status(thm)],[f54004,f1210]) ).
fof(f54060,plain,
! [X0,X1] :
( c_Public_Okeymode_OEncryption = X0
| hBOOL(hAPP(X1,X0))
| c_Public_Okeymode_OSignature = X0 ),
inference(resolution,[status(thm)],[f54035,f1210]) ).
fof(f54084,plain,
! [X0] :
( c_Public_Okeymode_OEncryption = X0
| c_Public_Okeymode_OSignature = X0 ),
inference(resolution,[status(thm)],[f54060,f1815]) ).
fof(f54118,plain,
! [X0,X1] : c_Public_Okeymode_OEncryption = c_List_Olist_OCons(X0,c_Public_Okeymode_OSignature,X1),
inference(resolution,[status(thm)],[f54084,f1171]) ).
fof(f54129,plain,
! [X0,X1] :
( c_Public_Okeymode_OEncryption = X0
| c_Public_Okeymode_OEncryption = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f54084,f54084]) ).
fof(f54347,plain,
! [X0] : c_Public_Okeymode_OEncryption != c_List_Olist_ONil(X0),
inference(paramodulation,[status(thm)],[f54118,f1174]) ).
fof(f54420,plain,
! [X0,X1,X2] :
( c_Public_Okeymode_OEncryption = c_List_Olist_OCons(X1,X2,X0)
| c_Public_Okeymode_OEncryption = c_List_Olist_ONil(X0) ),
inference(resolution,[status(thm)],[f54129,f1174]) ).
fof(f54851,plain,
! [X0,X1,X2] : c_Public_Okeymode_OEncryption = c_List_Olist_OCons(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f54420,f54347]) ).
fof(f54975,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| c_List_Olist_OCons(X0,X1,X2) != c_Public_Okeymode_OEncryption ),
inference(backward_demodulation,[status(thm)],[f54851,f1237]) ).
fof(f55023,plain,
! [X0,X1] :
( X0 = X1
| c_Public_Okeymode_OEncryption != c_Public_Okeymode_OEncryption ),
inference(forward_demodulation,[status(thm)],[f54851,f54975]) ).
fof(f55024,plain,
! [X0,X1] : X0 = X1,
inference(trivial_equality_resolution,[status(thm)],[f55023]) ).
fof(f55254,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f54347,f55024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV751-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 09:26:36 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.43 % Drodi V4.1.1
% 36.09/5.11 % Refutation found
% 36.09/5.11 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 36.09/5.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.69/5.34 % Elapsed time: 4.966438 seconds
% 2.69/5.34 % CPU time: 37.855661 seconds
% 2.69/5.34 % Total memory used: 655.310 MB
% 2.69/5.34 % Net memory used: 618.686 MB
%------------------------------------------------------------------------------