%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV757-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:49:29 PM UTC 2026
% Result : Unsatisfiable 59.11s 8.01s
% Output : CNFRefutation 24.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 66 ( 36 unt; 0 def)
% Number of atoms : 104 ( 45 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 42 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-4 aty)
% Number of variables : 197 ( 197 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,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(f64,axiom,
! [T_a] : c_List_Oset(c_List_Olist_ONil(T_a),T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,axiom,
! [V_x,V_xa,T_a] : c_List_Olist_OCons(V_x,V_xa,T_a) != c_List_Olist_ONil(T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f153,axiom,
! [V_a,V_A,T_a] : c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f167,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(f225,axiom,
! [V_A,V_H] : hBOOL(c_in(c_Message_Omsg_OAgent(V_A),c_Message_Osynth(V_H),tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f330,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(f331,axiom,
! [V_f,V_a,V_B,T_b,T_a] : c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f333,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(f338,axiom,
! [V_y,V_A,T_a,V_x] :
( ~ hBOOL(hAPP(V_A,V_x))
| hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f347,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(f402,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(f442,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(f493,axiom,
! [V_X,V_H] :
( ~ hBOOL(c_in(V_X,V_H,tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f527,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(f528,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(f629,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)],[f31]) ).
fof(f630,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)],[f629]) ).
fof(f670,plain,
! [X0] : c_List_Oset(c_List_Olist_ONil(X0),X0) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f721,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f803,plain,
! [X0,X1,X2] : c_Set_Oinsert(X0,X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f822,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f901,plain,
! [X0,X1] : hBOOL(c_in(c_Message_Omsg_OAgent(X0),c_Message_Osynth(X1),tc_Message_Omsg)),
inference(cnf_transformation,[status(thm)],[f225]) ).
fof(f1038,plain,
! [X0,X1,X2] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X0)),
inference(cnf_transformation,[status(thm)],[f330]) ).
fof(f1039,plain,
! [X0,X1,X2,X3,X4] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) = c_Set_Oinsert(hAPP(X0,X1),c_Set_Oimage(X0,X2,X3,X4),X4),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f1041,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)],[f333]) ).
fof(f1042,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)],[f1041]) ).
fof(f1049,plain,
! [V_A,V_x] :
( ~ hBOOL(hAPP(V_A,V_x))
| ! [V_y,T_a] : hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ),
inference(miniscoping,[status(thm)],[f338]) ).
fof(f1050,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f1049]) ).
fof(f1062,plain,
! [X0,X1,X2] :
( ~ hBOOL(c_in(X0,X1,X2))
| c_Set_Oinsert(X0,X1,X2) = X1 ),
inference(cnf_transformation,[status(thm)],[f347]) ).
fof(f1140,plain,
! [X0,X1,X2] : X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(thm)],[f402]) ).
fof(f1200,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)],[f442]) ).
fof(f1201,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)],[f1200]) ).
fof(f1284,plain,
! [X0,X1] :
( ~ hBOOL(c_in(X0,X1,tc_Message_Omsg))
| hBOOL(c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)) ),
inference(cnf_transformation,[status(thm)],[f493]) ).
fof(f1330,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)],[f527]) ).
fof(f1331,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f1330]) ).
fof(f1332,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)],[f528]) ).
fof(f1333,plain,
! [X0,X1,X2] :
( ~ hBOOL(c_in(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1332]) ).
fof(f1675,plain,
! [X0,X1] : hBOOL(hAPP(c_Message_Osynth(X0),c_Message_Omsg_OAgent(X1))),
inference(resolution,[status(thm)],[f1333,f901]) ).
fof(f1720,plain,
! [X0,X1,X2] : hBOOL(c_in(c_Message_Omsg_OAgent(X0),c_Message_Osynth(X1),X2)),
inference(resolution,[status(thm)],[f1675,f1331]) ).
fof(f1868,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,X0,X1),c_Public_Okeymode_OSignature))
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,X0,X1),X2)) ),
inference(resolution,[status(thm)],[f1038,f630]) ).
fof(f1869,plain,
! [X0,X1,X2,X3] : hBOOL(c_in(X0,c_Set_Oinsert(X0,X1,X2),X3)),
inference(resolution,[status(thm)],[f1038,f1331]) ).
fof(f2097,plain,
! [X0,X1] : hBOOL(c_in(c_Message_Omsg_OAgent(X0),c_Message_Oparts(c_Message_Osynth(X1)),tc_Message_Omsg)),
inference(resolution,[status(thm)],[f1284,f1720]) ).
fof(f2355,plain,
! [X0,X1] : hBOOL(hAPP(c_Message_Oparts(c_Message_Osynth(X0)),c_Message_Omsg_OAgent(X1))),
inference(resolution,[status(thm)],[f2097,f1333]) ).
fof(f2361,plain,
! [X0,X1,X2] : hBOOL(c_in(c_Message_Omsg_OAgent(X0),c_Message_Oparts(c_Message_Osynth(X1)),X2)),
inference(resolution,[status(thm)],[f2355,f1331]) ).
fof(f2982,plain,
! [X0,X1,X2] : c_Set_Oinsert(X0,X1,X2) != c_List_Oset(c_List_Olist_ONil(X2),X2),
inference(paramodulation,[status(thm)],[f670,f803]) ).
fof(f3006,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_List_Oset(c_List_Olist_ONil(X0),X0),X1)),
inference(paramodulation,[status(thm)],[f670,f822]) ).
fof(f4488,plain,
! [X0,X1,X2] : c_Set_Oinsert(c_Message_Omsg_OAgent(X0),c_Message_Oparts(c_Message_Osynth(X1)),X2) = c_Message_Oparts(c_Message_Osynth(X1)),
inference(resolution,[status(thm)],[f1062,f2361]) ).
fof(f4504,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)],[f1062,f1869]) ).
fof(f5029,plain,
! [X0,X1,X2,X3] : c_Set_Oinsert(X0,X1,X2) != c_List_Oset(c_List_Olist_ONil(X3),X3),
inference(paramodulation,[status(thm)],[f4504,f2982]) ).
fof(f14052,plain,
! [X0,X1,X2,X3,X4] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,X2,X3),X4),X1)),
inference(resolution,[status(thm)],[f1050,f1038]) ).
fof(f18650,plain,
! [X0,X1,X2,X3,X4,X5] : c_Set_Oimage(X0,c_Set_Oinsert(X1,X2,X3),X3,X4) != c_List_Oset(c_List_Olist_ONil(X5),X5),
inference(paramodulation,[status(thm)],[f1039,f5029]) ).
fof(f23471,plain,
! [X0,X1,X2,X3,X4] : c_Set_Oimage(X0,c_Message_Oparts(c_Message_Osynth(X1)),X2,X3) != c_List_Oset(c_List_Olist_ONil(X4),X4),
inference(paramodulation,[status(thm)],[f4488,f18650]) ).
fof(f35104,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,c_Set_Oinsert(c_Public_Okeymode_OSignature,X0,X1),X2),X3)),
inference(resolution,[status(thm)],[f1868,f14052]) ).
fof(f35370,plain,
! [X0,X1,X2] :
( c_Public_Okeymode_OEncryption = X2
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,X0,X1),X2)) ),
inference(resolution,[status(thm)],[f35104,f1042]) ).
fof(f35385,plain,
! [X0,X1] :
( c_Public_Okeymode_OSignature = X0
| hBOOL(hAPP(X1,X0))
| c_Public_Okeymode_OEncryption = X0 ),
inference(resolution,[status(thm)],[f35370,f1042]) ).
fof(f35401,plain,
! [X0] :
( c_Public_Okeymode_OSignature = X0
| c_Public_Okeymode_OEncryption = X0 ),
inference(resolution,[status(thm)],[f35385,f3006]) ).
fof(f35425,plain,
! [X0,X1] : c_Public_Okeymode_OSignature = c_List_Olist_OCons(X0,c_Public_Okeymode_OEncryption,X1),
inference(resolution,[status(thm)],[f35401,f1140]) ).
fof(f35439,plain,
! [X0,X1] :
( c_Public_Okeymode_OSignature = X0
| c_Public_Okeymode_OSignature = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f35401,f35401]) ).
fof(f35990,plain,
! [X0] : c_Public_Okeymode_OSignature != c_List_Olist_ONil(X0),
inference(paramodulation,[status(thm)],[f35425,f721]) ).
fof(f36115,plain,
! [X0,X1,X2] :
( c_Public_Okeymode_OSignature = c_List_Olist_OCons(X1,X2,X0)
| c_Public_Okeymode_OSignature = c_List_Olist_ONil(X0) ),
inference(resolution,[status(thm)],[f35439,f721]) ).
fof(f36415,plain,
! [X0,X1,X2] : c_Public_Okeymode_OSignature = c_List_Olist_OCons(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f36115,f35990]) ).
fof(f36462,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| c_List_Olist_OCons(X0,X1,X2) != c_Public_Okeymode_OSignature ),
inference(backward_demodulation,[status(thm)],[f36415,f1201]) ).
fof(f36469,plain,
! [X0,X1] :
( X0 = X1
| c_Public_Okeymode_OSignature != c_Public_Okeymode_OSignature ),
inference(forward_demodulation,[status(thm)],[f36415,f36462]) ).
fof(f36470,plain,
! [X0,X1] : X0 = X1,
inference(trivial_equality_resolution,[status(thm)],[f36469]) ).
fof(f36476,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f23471,f36470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV757-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.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 09:26:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.02/0.41 % Drodi V4.1.1
% 59.11/8.01 % Refutation found
% 59.11/8.01 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 59.11/8.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.68/8.97 % Elapsed time: 8.589106 seconds
% 3.68/8.97 % CPU time: 61.933546 seconds
% 3.68/8.97 % Total memory used: 627.660 MB
% 3.68/8.97 % Net memory used: 589.767 MB
%------------------------------------------------------------------------------