%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW353+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 03:07:42 PM UTC 2026
% Result : Theorem 133.44s 18.01s
% Output : CNFRefutation 134.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 10 unt; 1 def)
% Number of atoms : 56 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 21 ~; 16 |; 3 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [V_ts_2,V_t_2,V_Ga_2,T_a] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
& c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T_b,V_y_2,T_a,V_x_2,V_f_2] :
( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2)
=> hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f161,axiom,
! [V_b_2,V_B_2,V_a_2,T_a] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2))
=> V_a_2 = V_b_2 )
=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5243,hypothesis,
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5244,hypothesis,
hAPP(c_Com_Obody,v_pname) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5245,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,v_pname))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5246,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,v_pname))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(negated_conjecture,[status(cth)],[f5245]) ).
fof(f5258,plain,
! [V_ts_2,V_t_2,V_Ga_2,T_a] :
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2)
& c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f5259,plain,
! [X0,X1,X2,X3] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X2),X3))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X0)),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_HOL_Obool)))) ),
inference(cnf_transformation,[status(thm)],[f5258]) ).
fof(f5261,plain,
! [T_b,V_y_2,T_a,V_x_2,V_f_2] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2)
| hAPP(V_f_2,V_x_2) != hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f5262,plain,
! [T_a,V_x_2,V_f_2] :
( ! [T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2)
| ! [V_y_2] : hAPP(V_f_2,V_x_2) != hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ),
inference(miniscoping,[status(thm)],[f5261]) ).
fof(f5263,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Map_Odom(X4,X2,X0)) = c_Map_Odom(X4,X2,X0)
| hAPP(X0,X1) != hAPP(c_Option_Ooption_OSome(X2),X3) ),
inference(cnf_transformation,[status(thm)],[f5262]) ).
fof(f5675,plain,
! [V_b_2,V_B_2,V_a_2,T_a] :
( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2)))
| ( V_a_2 != V_b_2
& ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f161]) ).
fof(f5677,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X0),hAPP(hAPP(c_Set_Oinsert(X2),X1),X3)))
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f5675]) ).
fof(f19977,plain,
! [B_x] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ),
inference(pre_NNF_transformation,[status(thm)],[f5243]) ).
fof(f19978,plain,
! [X0] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,X0))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ),
inference(cnf_transformation,[status(thm)],[f19977]) ).
fof(f19979,plain,
hAPP(c_Com_Obody,v_pname) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(cnf_transformation,[status(thm)],[f5244]) ).
fof(f19980,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,v_pname))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(cnf_transformation,[status(thm)],[f5246]) ).
fof(f20362,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))),
inference(destructive_equality_resolution,[status(thm)],[f5677]) ).
fof(f20846,plain,
! [X0] : ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,v_pname))),X0)),
inference(resolution,[status(thm)],[f5259,f19980]) ).
fof(f23517,definition,
( sQ40_spl
<=> c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody) = hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f23518,plain,
( ~ sQ40_spl
| hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)) = c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody) ),
inference(component_clause,[status(thm)],[f23517]) ).
fof(f23519,plain,
( sQ40_spl
| c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody) != hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)) ),
inference(component_clause,[status(thm)],[f23517]) ).
fof(f23813,plain,
( ~ sQ40_spl
| hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ),
inference(paramodulation,[status(thm)],[f23518,f20362]) ).
fof(f23900,plain,
( ~ sQ40_spl
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,v_pname))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
inference(resolution,[status(thm)],[f23813,f19978]) ).
fof(f23906,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23900,f20846]) ).
fof(f23907,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f23906]) ).
fof(f24696,plain,
! [X0] :
( sQ40_spl
| hAPP(c_Com_Obody,v_pname) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),X0) ),
inference(resolution,[status(thm)],[f5263,f23519]) ).
fof(f31289,plain,
( sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19979,f24696]) ).
fof(f31290,plain,
sQ40_spl,
inference(contradiction_clause,[status(thm)],[f31289]) ).
fof(f31291,plain,
$false,
inference(sat_refutation,[status(thm)],[f23907,f31290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW353+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n009.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 21 09:48:58 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.79/1.08 % Drodi V4.1.1
% 133.44/18.01 % Refutation found
% 133.44/18.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 133.44/18.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 69.68/18.30 % Elapsed time: 17.892165 seconds
% 69.68/18.30 % CPU time: 135.517613 seconds
% 69.68/18.30 % Total memory used: 1.255 GB
% 69.68/18.30 % Net memory used: 1.222 GB
%------------------------------------------------------------------------------