%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV759-1 : 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 101.23s 13.48s
% Output : CNFRefutation 95.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 61 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 24 ~; 27 |; 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 : 92 ( 92 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,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(f64,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(f133,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(f388,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(f390,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(f392,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f465,axiom,
! [V_x,V_t,T_a] : c_List_Olist_OCons(V_x,V_t,T_a) != V_t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f584,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(f670,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)],[f25]) ).
fof(f671,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ hBOOL(c_in(X0,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)) ),
inference(cnf_transformation,[status(thm)],[f670]) ).
fof(f719,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)],[f64]) ).
fof(f720,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(X0,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,c_Public_Okeymode_OSignature)) ),
inference(cnf_transformation,[status(thm)],[f719]) ).
fof(f822,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f1178,plain,
! [X0,X1,X2] : hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X0)),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f1180,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)],[f390]) ).
fof(f1181,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X1,X3))
| X0 = X3
| ~ hBOOL(hAPP(c_Set_Oinsert(X0,X1,X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f1180]) ).
fof(f1183,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)],[f392]) ).
fof(f1290,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) != X1,
inference(cnf_transformation,[status(thm)],[f465]) ).
fof(f1462,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)],[f584]) ).
fof(f1463,plain,
! [X0,X1,X2] :
( hBOOL(c_in(X1,X0,X2))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1462]) ).
fof(f1685,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)],[f1178,f720]) ).
fof(f13219,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(c_Set_Oinsert(X0,c_Set_Oinsert(X1,X2,X3),X3),X1)),
inference(paramodulation,[status(thm)],[f1183,f1178]) ).
fof(f24472,plain,
! [X0,X1,X2] :
( X2 = X0
| ~ hBOOL(hAPP(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X2)) ),
inference(resolution,[status(thm)],[f671,f1463]) ).
fof(f50456,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)],[f1685,f13219]) ).
fof(f50601,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,X1,X2),X0))
| X0 = c_Public_Okeymode_OSignature ),
inference(resolution,[status(thm)],[f50456,f1181]) ).
fof(f50663,plain,
! [X0] :
( X0 = c_Public_Okeymode_OSignature
| c_Public_Okeymode_OEncryption = X0 ),
inference(resolution,[status(thm)],[f50601,f24472]) ).
fof(f50736,plain,
! [X0,X1] : c_List_Olist_OCons(X0,c_Public_Okeymode_OSignature,X1) = c_Public_Okeymode_OEncryption,
inference(resolution,[status(thm)],[f50663,f1290]) ).
fof(f50740,plain,
! [X0,X1] :
( X1 = X0
| X1 = c_Public_Okeymode_OEncryption
| c_Public_Okeymode_OEncryption = X0 ),
inference(paramodulation,[status(thm)],[f50663,f50663]) ).
fof(f50805,plain,
! [X0] : c_List_Olist_ONil(X0) != c_Public_Okeymode_OEncryption,
inference(paramodulation,[status(thm)],[f50736,f822]) ).
fof(f50809,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_Public_Okeymode_OEncryption = X0
| c_Public_Okeymode_OEncryption != c_Public_Okeymode_OEncryption ),
inference(paramodulation,[status(thm)],[f50740,f50805]) ).
fof(f50810,plain,
! [X0,X1] :
( c_Public_Okeymode_OEncryption = X1
| c_List_Olist_ONil(X0) = X1 ),
inference(trivial_equality_resolution,[status(thm)],[f50809]) ).
fof(f50816,plain,
! [X0,X1,X2] : c_List_Olist_OCons(X0,X1,X2) = c_Public_Okeymode_OEncryption,
inference(resolution,[status(thm)],[f50810,f822]) ).
fof(f50899,plain,
! [X0] : c_Public_Okeymode_OEncryption != X0,
inference(backward_demodulation,[status(thm)],[f50816,f1290]) ).
fof(f50905,plain,
$false,
inference(destructive_equality_resolution,[status(thm)],[f50899]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV759-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n026.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 09:26:37 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.22/0.59 % Drodi V4.1.1
% 101.23/13.48 % Refutation found
% 101.23/13.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 101.23/13.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.76/14.15 % Elapsed time: 13.657628 seconds
% 5.76/14.15 % CPU time: 103.625154 seconds
% 5.76/14.15 % Total memory used: 898.143 MB
% 5.76/14.15 % Net memory used: 858.528 MB
%------------------------------------------------------------------------------