%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV905-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:49:45 PM UTC 2026
% Result : Unsatisfiable 2.53s 0.83s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 23 unt; 0 def)
% Number of atoms : 81 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 67 ( 34 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-4 aty)
% Number of variables : 89 ( 89 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [V_m,V_n,T_b,T_a,V_k] :
( hAPP(V_m,V_k) = c_Option_Ooption_ONone(T_a)
| hAPP(c_Map_Omap__add(V_m,V_n,T_b,T_a),V_k) != c_Option_Ooption_ONone(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [V_A,V_B,T_a] : c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f149,axiom,
! [V_c,V_A,V_B,T_a] :
( ~ hBOOL(c_in(V_c,V_B,T_a))
| hBOOL(c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f385,axiom,
! [V_l1,V_l2,T_a,T_b,V_m] :
( ~ hBOOL(c_in(V_m,c_Map_Odom(V_l2,T_a,T_b),T_a))
| hAPP(c_Map_Omap__add(V_l1,V_l2,T_a,T_b),V_m) = hAPP(V_l2,V_m) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f398,axiom,
! [V_pn] :
( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(c_Com_Ocom_OBODY(V_pn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f415,axiom,
! [V_c] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(V_c)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f422,axiom,
! [T_a,V_x] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f434,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/sandbox/benchmark/theBenchmark.p') ).
fof(f435,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/sandbox/benchmark/theBenchmark.p') ).
fof(f445,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f446,negated_conjecture,
c_Com_OWT__bodies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f448,negated_conjecture,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f449,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f491,plain,
! [V_m,T_a,V_k] :
( hAPP(V_m,V_k) = c_Option_Ooption_ONone(T_a)
| ! [V_n,T_b] : hAPP(c_Map_Omap__add(V_m,V_n,T_b,T_a),V_k) != c_Option_Ooption_ONone(T_a) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f492,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(X0,X4) = c_Option_Ooption_ONone(X3)
| hAPP(c_Map_Omap__add(X0,X1,X2,X3),X4) != c_Option_Ooption_ONone(X3) ),
inference(cnf_transformation,[status(thm)],[f491]) ).
fof(f518,plain,
! [X0,X1,X2] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,tc_bool)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f734,plain,
! [V_c,V_B,T_a] :
( ~ hBOOL(c_in(V_c,V_B,T_a))
| ! [V_A] : hBOOL(c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)) ),
inference(miniscoping,[status(thm)],[f149]) ).
fof(f735,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(c_in(X0,X2,X3))
| hBOOL(c_in(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_fun(X3,tc_bool)),X3)) ),
inference(cnf_transformation,[status(thm)],[f734]) ).
fof(f1111,plain,
! [V_l2,T_a,T_b,V_m] :
( ~ hBOOL(c_in(V_m,c_Map_Odom(V_l2,T_a,T_b),T_a))
| ! [V_l1] : hAPP(c_Map_Omap__add(V_l1,V_l2,T_a,T_b),V_m) = hAPP(V_l2,V_m) ),
inference(miniscoping,[status(thm)],[f385]) ).
fof(f1112,plain,
! [X0,X1,X2,X3,X4] :
( ~ hBOOL(c_in(X4,c_Map_Odom(X1,X2,X3),X2))
| hAPP(c_Map_Omap__add(X0,X1,X2,X3),X4) = hAPP(X1,X4) ),
inference(cnf_transformation,[status(thm)],[f1111]) ).
fof(f1131,plain,
! [X0] :
( hAPP(c_Com_Obody,X0) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Com_OWT(c_Com_Ocom_OBODY(X0)) ),
inference(cnf_transformation,[status(thm)],[f398]) ).
fof(f1157,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ! [V_c] :
( ~ c_Com_OWT(V_c)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f1158,plain,
! [X0] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(X0)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X0),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(cnf_transformation,[status(thm)],[f1157]) ).
fof(f1169,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[status(thm)],[f422]) ).
fof(f1184,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)],[f434]) ).
fof(f1185,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f1184]) ).
fof(f1186,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)],[f435]) ).
fof(f1187,plain,
! [X0,X1,X2] :
( ~ hBOOL(c_in(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f1186]) ).
fof(f1202,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(cnf_transformation,[status(thm)],[f445]) ).
fof(f1203,plain,
c_Com_OWT__bodies,
inference(cnf_transformation,[status(thm)],[f446]) ).
fof(f1205,plain,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
inference(cnf_transformation,[status(thm)],[f448]) ).
fof(f1206,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f1311,plain,
hBOOL(hAPP(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),v_x)),
inference(resolution,[status(thm)],[f1187,f1205]) ).
fof(f1328,plain,
! [X0] : hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),X0)),
inference(resolution,[status(thm)],[f1311,f1185]) ).
fof(f1330,plain,
! [X0,X1] : hBOOL(c_in(v_x,c_Lattices_Oupper__semilattice__class_Osup(X0,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_fun(X1,tc_bool)),X1)),
inference(resolution,[status(thm)],[f1328,f735]) ).
fof(f1892,plain,
! [X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_fun(X1,tc_bool)),v_x)),
inference(resolution,[status(thm)],[f1330,f1187]) ).
fof(f1905,plain,
! [X0,X1] : hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),X0,tc_fun(X1,tc_bool)),v_x)),
inference(paramodulation,[status(thm)],[f518,f1892]) ).
fof(f2646,plain,
! [X0] : hAPP(c_Map_Omap__add(X0,c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),v_x) = hAPP(c_Com_Obody,v_x),
inference(resolution,[status(thm)],[f1112,f1328]) ).
fof(f2682,plain,
! [X0] :
( hAPP(X0,v_x) = c_Option_Ooption_ONone(tc_Com_Ocom)
| hAPP(c_Com_Obody,v_x) != c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(paramodulation,[status(thm)],[f2646,f492]) ).
fof(f2736,plain,
! [X0] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT(X0)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(X0),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(forward_subsumption_resolution,[status(thm)],[f1158,f1203]) ).
fof(f2738,plain,
! [X0] :
( hAPP(c_Com_Obody,X0) = c_Option_Ooption_ONone(tc_Com_Ocom)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(resolution,[status(thm)],[f2736,f1131]) ).
fof(f2741,plain,
! [X0] :
( hAPP(c_Com_Obody,X0) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OBODY(X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(forward_subsumption_resolution,[status(thm)],[f2738,f1202]) ).
fof(f2845,plain,
hAPP(c_Com_Obody,v_x) = c_Option_Ooption_ONone(tc_Com_Ocom),
inference(resolution,[status(thm)],[f2741,f1206]) ).
fof(f2851,plain,
! [X0] :
( hAPP(X0,v_x) = c_Option_Ooption_ONone(tc_Com_Ocom)
| c_Option_Ooption_ONone(tc_Com_Ocom) != c_Option_Ooption_ONone(tc_Com_Ocom) ),
inference(backward_demodulation,[status(thm)],[f2845,f2682]) ).
fof(f2859,plain,
! [X0] : hAPP(X0,v_x) = c_Option_Ooption_ONone(tc_Com_Ocom),
inference(trivial_equality_resolution,[status(thm)],[f2851]) ).
fof(f2860,plain,
hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom)),
inference(backward_demodulation,[status(thm)],[f2859,f1905]) ).
fof(f2878,plain,
~ hBOOL(c_Option_Ooption_ONone(tc_Com_Ocom)),
inference(paramodulation,[status(thm)],[f2859,f1169]) ).
fof(f2981,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2878,f2860]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV905-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41 % Computer : n014.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Mon Sep 21 09:31:04 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.48 % Drodi V4.1.1
% 2.53/0.83 % Refutation found
% 2.53/0.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.53/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.53/0.86 % Elapsed time: 0.435897 seconds
% 2.53/0.86 % CPU time: 2.812049 seconds
% 2.53/0.86 % Total memory used: 159.703 MB
% 2.53/0.86 % Net memory used: 156.842 MB
%------------------------------------------------------------------------------