%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV752-1 : 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 02:49:28 PM UTC 2026
% Result : Unsatisfiable 115.89s 15.16s
% Output : CNFRefutation 115.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 18 unt; 0 def)
% Number of atoms : 75 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 33 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 121 ( 121 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,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(f59,axiom,
! [V_b,V_a,T_a] :
( ~ 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(f371,axiom,
! [V_a,V_A,T_a,V_b] :
( ~ c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)
| V_a = V_b
| c_in(V_a,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f383,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(f389,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(f393,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(f431,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(f534,axiom,
! [V_x,V_S,T_a] :
( ~ hBOOL(hAPP(V_S,V_x))
| c_in(V_x,V_S,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f535,axiom,
! [V_S,V_x,T_a] :
( ~ c_in(V_x,V_S,T_a)
| hBOOL(hAPP(V_S,V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f617,plain,
c_Public_Okeymode_OSignature != c_Public_Okeymode_OEncryption,
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f620,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)],[f29]) ).
fof(f621,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)],[f620]) ).
fof(f659,plain,
! [V_b,V_a] :
( ! [T_a] : ~ 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)],[f59]) ).
fof(f660,plain,
! [X0,X1,X2] :
( ~ 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)],[f659]) ).
fof(f1102,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X0,c_Set_Oinsert(X3,X1,X2),X2)
| X0 = X3
| c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f1118,plain,
! [X0,X1,X2] : X0 != c_List_Olist_OCons(X1,X0,X2),
inference(cnf_transformation,[status(thm)],[f383]) ).
fof(f1124,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f1129,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)],[f393]) ).
fof(f1130,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f1129]) ).
fof(f1178,plain,
! [X0,X1,X2] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X0)),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f1332,plain,
! [V_x,V_S] :
( ~ hBOOL(hAPP(V_S,V_x))
| ! [T_a] : c_in(V_x,V_S,T_a) ),
inference(miniscoping,[status(thm)],[f534]) ).
fof(f1333,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X1,X0))
| c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1332]) ).
fof(f1334,plain,
! [V_S,V_x] :
( ! [T_a] : ~ c_in(V_x,V_S,T_a)
| hBOOL(hAPP(V_S,V_x)) ),
inference(miniscoping,[status(thm)],[f535]) ).
fof(f1335,plain,
! [X0,X1,X2] :
( ~ c_in(X1,X0,X2)
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1334]) ).
fof(f2217,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)],[f1178,f621]) ).
fof(f2748,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X1,X3)
| ~ c_in(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1335,f1333]) ).
fof(f3086,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X3)
| X0 = X1 ),
inference(resolution,[status(thm)],[f660,f2748]) ).
fof(f10664,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_in(X0,c_Set_Oinsert(X3,X1,X2),X4)
| X0 = X3
| c_in(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1102,f2748]) ).
fof(f10730,plain,
! [X0,X1,X2,X3,X4] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,X2,X3),X4),X1)),
inference(resolution,[status(thm)],[f1130,f1178]) ).
fof(f51095,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)],[f2217,f10730]) ).
fof(f51392,plain,
! [X0,X1,X2,X3,X4] : 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)],[f51095,f1333]) ).
fof(f51405,plain,
! [X0,X1,X2,X3] :
( X0 = c_Public_Okeymode_OEncryption
| c_in(X0,c_Set_Oinsert(c_Public_Okeymode_OSignature,X1,X2),X3) ),
inference(resolution,[status(thm)],[f51392,f10664]) ).
fof(f51423,plain,
! [X0] :
( X0 = c_Public_Okeymode_OSignature
| X0 = c_Public_Okeymode_OEncryption ),
inference(resolution,[status(thm)],[f51405,f3086]) ).
fof(f51444,plain,
! [X0,X1] : c_List_Olist_OCons(X0,c_Public_Okeymode_OSignature,X1) = c_Public_Okeymode_OEncryption,
inference(resolution,[status(thm)],[f51423,f1118]) ).
fof(f51445,plain,
! [X0,X1] :
( X1 = c_Public_Okeymode_OEncryption
| X0 = X1
| X0 = c_Public_Okeymode_OEncryption ),
inference(paramodulation,[status(thm)],[f51423,f51423]) ).
fof(f51506,plain,
! [X0] : c_Public_Okeymode_OEncryption != c_List_Olist_ONil(X0),
inference(paramodulation,[status(thm)],[f51444,f1124]) ).
fof(f52113,plain,
! [X0,X1] :
( X0 = c_List_Olist_ONil(X1)
| X0 = c_Public_Okeymode_OEncryption ),
inference(resolution,[status(thm)],[f51445,f51506]) ).
fof(f52144,plain,
! [X0] : c_Public_Okeymode_OSignature = c_List_Olist_ONil(X0),
inference(resolution,[status(thm)],[f52113,f617]) ).
fof(f52340,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) != c_Public_Okeymode_OSignature,
inference(backward_demodulation,[status(thm)],[f52144,f1124]) ).
fof(f53325,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) = c_Public_Okeymode_OEncryption,
inference(resolution,[status(thm)],[f52340,f51423]) ).
fof(f53383,plain,
! [X0] : X0 != c_Public_Okeymode_OEncryption,
inference(backward_demodulation,[status(thm)],[f53325,f1118]) ).
fof(f53399,plain,
$false,
inference(destructive_equality_resolution,[status(thm)],[f53383]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV752-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 09:18:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.43 % Drodi V4.1.1
% 115.89/15.16 % Refutation found
% 115.89/15.16 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 115.89/15.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.21/16.21 % Elapsed time: 15.836199 seconds
% 8.21/16.21 % CPU time: 118.252482 seconds
% 8.21/16.21 % Total memory used: 912.677 MB
% 8.21/16.21 % Net memory used: 864.280 MB
%------------------------------------------------------------------------------