%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV730-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:49:25 PM UTC 2026
% Result : Unsatisfiable 39.62s 5.47s
% Output : CNFRefutation 31.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 58 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 23 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 90 ( 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,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/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [V_b,V_a,T_a] :
( ~ hBOOL(c_in(V_b,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a))
| V_b = V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f367,axiom,
! [V_xs,V_x,T_a] : V_xs != c_List_Olist_OCons(V_x,V_xs,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f373,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/sandbox/benchmark/theBenchmark.p') ).
fof(f382,axiom,
! [V_x,V_y,V_A,T_a] : c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f398,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/sandbox/benchmark/theBenchmark.p') ).
fof(f415,axiom,
! [V_x,V_A,T_a] : hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f519,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/sandbox/benchmark/theBenchmark.p') ).
fof(f594,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)],[f25]) ).
fof(f595,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)],[f594]) ).
fof(f628,plain,
! [V_b,V_a] :
( ! [T_a] : ~ hBOOL(c_in(V_b,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a))
| V_b = V_a ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f629,plain,
! [X0,X1,X2] :
( ~ hBOOL(c_in(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f628]) ).
fof(f1074,plain,
! [X0,X1,X2] : X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(thm)],[f367]) ).
fof(f1080,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f1091,plain,
! [X0,X1,X2,X3] : c_Set_Oinsert(X0,c_Set_Oinsert(X1,X2,X3),X3) = c_Set_Oinsert(X1,c_Set_Oinsert(X0,X2,X3),X3),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f1112,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)],[f398]) ).
fof(f1113,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)],[f1112]) ).
fof(f1134,plain,
! [X0,X1,X2] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X0)),
inference(cnf_transformation,[status(thm)],[f415]) ).
fof(f1280,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)],[f519]) ).
fof(f1281,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f1280]) ).
fof(f1754,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)],[f1134,f595]) ).
fof(f3097,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X0))
| X0 = X1 ),
inference(resolution,[status(thm)],[f629,f1281]) ).
fof(f12644,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,X2,X3),X3),X1)),
inference(paramodulation,[status(thm)],[f1091,f1134]) ).
fof(f46149,plain,
! [X0,X1,X2] : hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,c_Set_Oinsert(c_Public_Okeymode_OEncryption,X0,X1),X1),X2)),
inference(resolution,[status(thm)],[f1754,f12644]) ).
fof(f46513,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)],[f46149,f1113]) ).
fof(f46544,plain,
! [X0] :
( X0 = c_Public_Okeymode_OEncryption
| c_Public_Okeymode_OSignature = X0 ),
inference(resolution,[status(thm)],[f46513,f3097]) ).
fof(f46572,plain,
! [X0,X1] : c_List_Olist_OCons(X0,c_Public_Okeymode_OSignature,X1) = c_Public_Okeymode_OEncryption,
inference(resolution,[status(thm)],[f46544,f1074]) ).
fof(f46576,plain,
! [X0,X1] :
( X0 = c_Public_Okeymode_OEncryption
| X1 = c_Public_Okeymode_OEncryption
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f46544,f46544]) ).
fof(f46616,plain,
! [X0] : c_Public_Okeymode_OEncryption != c_List_Olist_ONil(X0),
inference(paramodulation,[status(thm)],[f46572,f1080]) ).
fof(f46754,plain,
! [X0,X1] :
( X0 = c_Public_Okeymode_OEncryption
| X0 = c_List_Olist_ONil(X1) ),
inference(resolution,[status(thm)],[f46576,f46616]) ).
fof(f46786,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) = c_Public_Okeymode_OEncryption,
inference(resolution,[status(thm)],[f46754,f1080]) ).
fof(f46858,plain,
! [X0] : X0 != c_Public_Okeymode_OEncryption,
inference(backward_demodulation,[status(thm)],[f46786,f1074]) ).
fof(f46866,plain,
$false,
inference(destructive_equality_resolution,[status(thm)],[f46858]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV730-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.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 : Mon Sep 21 09:17:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 39.62/5.47 % Refutation found
% 39.62/5.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 39.62/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.54/6.48 % Elapsed time: 6.100849 seconds
% 3.54/6.48 % CPU time: 41.809398 seconds
% 3.54/6.48 % Total memory used: 725.343 MB
% 3.54/6.48 % Net memory used: 693.560 MB
%------------------------------------------------------------------------------