%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV742-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 02:49:26 PM UTC 2026
% Result : Unsatisfiable 111.12s 14.68s
% Output : CNFRefutation 78.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 18 unt; 0 def)
% Number of atoms : 62 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 27 ~; 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 : 99 ( 99 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f61,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f398,axiom,
! [V_a,V_A,T_a,V_b] :
( ~ hBOOL(c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a))
| V_a = V_b
| hBOOL(c_in(V_a,V_A,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f409,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(f416,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(f455,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(f554,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(f644,plain,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f648,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(f649,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)],[f648]) ).
fof(f687,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)],[f61]) ).
fof(f688,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)],[f687]) ).
fof(f1153,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(c_in(X0,c_Set_Oinsert(X3,X1,X2),X2))
| X0 = X3
| hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f398]) ).
fof(f1168,plain,
! [X0,X1,X2] : X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(thm)],[f409]) ).
fof(f1172,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(thm)],[f413]) ).
fof(f1176,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)],[f416]) ).
fof(f1177,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f1176]) ).
fof(f1224,plain,
! [X0,X1,X2] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X0)),
inference(cnf_transformation,[status(thm)],[f455]) ).
fof(f1379,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)],[f554]) ).
fof(f1380,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f1379]) ).
fof(f2359,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)],[f1224,f649]) ).
fof(f7492,plain,
! [X0,X1,X2,X3,X4] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,X2,X3),X4),X1)),
inference(resolution,[status(thm)],[f1177,f1224]) ).
fof(f38755,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)],[f2359,f7492]) ).
fof(f39067,plain,
! [X0,X1,X2,X3,X4] : hBOOL(c_in(X0,c_Set_Oinsert(c_Public_Okeymode_OEncryption,c_Set_Oinsert(c_Public_Okeymode_OSignature,X1,X2),X3),X4)),
inference(resolution,[status(thm)],[f38755,f1380]) ).
fof(f43663,plain,
! [X0,X1,X2,X3] :
( X0 = c_Public_Okeymode_OEncryption
| hBOOL(c_in(X0,c_Set_Oinsert(c_Public_Okeymode_OSignature,X1,X2),X3)) ),
inference(resolution,[status(thm)],[f39067,f1153]) ).
fof(f44454,plain,
! [X0] :
( X0 = c_Public_Okeymode_OSignature
| X0 = c_Public_Okeymode_OEncryption ),
inference(resolution,[status(thm)],[f43663,f688]) ).
fof(f44475,plain,
! [X0,X1] : c_List_Olist_OCons(X0,c_Public_Okeymode_OEncryption,X1) = c_Public_Okeymode_OSignature,
inference(resolution,[status(thm)],[f44454,f1168]) ).
fof(f44476,plain,
! [X0,X1] :
( X1 = c_Public_Okeymode_OSignature
| X0 = c_Public_Okeymode_OSignature
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f44454,f44454]) ).
fof(f44536,plain,
! [X0] : c_Public_Okeymode_OSignature != c_List_Olist_ONil(X0),
inference(paramodulation,[status(thm)],[f44475,f1172]) ).
fof(f44545,plain,
! [X0,X1] :
( X0 = c_Public_Okeymode_OSignature
| X0 = c_List_Olist_ONil(X1) ),
inference(resolution,[status(thm)],[f44476,f44536]) ).
fof(f44574,plain,
! [X0] : c_Public_Okeymode_OEncryption = c_List_Olist_ONil(X0),
inference(resolution,[status(thm)],[f44545,f644]) ).
fof(f44866,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) != c_Public_Okeymode_OEncryption,
inference(backward_demodulation,[status(thm)],[f44574,f1172]) ).
fof(f45088,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) = c_Public_Okeymode_OSignature,
inference(resolution,[status(thm)],[f44866,f44454]) ).
fof(f45161,plain,
! [X0] : X0 != c_Public_Okeymode_OSignature,
inference(backward_demodulation,[status(thm)],[f45088,f1168]) ).
fof(f45173,plain,
$false,
inference(destructive_equality_resolution,[status(thm)],[f45161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV742-1 : 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 : n011.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 09:23:11 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.43 % Drodi V4.1.1
% 111.12/14.68 % Refutation found
% 111.12/14.68 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 111.12/14.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.15/15.28 % Elapsed time: 14.905577 seconds
% 10.15/15.28 % CPU time: 113.367083 seconds
% 10.15/15.28 % Total memory used: 837.518 MB
% 10.15/15.28 % Net memory used: 801.228 MB
%------------------------------------------------------------------------------