%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW360+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 : 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 03:07:43 PM UTC 2026
% Result : Theorem 28.66s 4.66s
% Output : CNFRefutation 28.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 16 unt; 0 def)
% Number of atoms : 66 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 25 ~; 17 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 82 ( 81 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_G_2,V_ts_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),V_ts_2),V_G_2))
=> v_P(V_G_2,V_ts_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f106,axiom,
! [V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,axiom,
! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f121,axiom,
! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f125,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f135,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5226,conjecture,
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_U))
=> v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,B_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5227,negated_conjecture,
~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_U))
=> v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,B_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
inference(negated_conjecture,[status(cth)],[f5226]) ).
fof(f5243,plain,
! [X0,X1,X2,X3,X4] : hAPP(c_Set_Oimage(X0,X1,X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X0,X1,X2),X4)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f5244,plain,
! [V_G_2,V_ts_2] :
( v_P(V_G_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),V_ts_2),V_G_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f5245,plain,
! [X0,X1] :
( v_P(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f5244]) ).
fof(f5562,plain,
! [V_A_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f5563,plain,
( ! [V_A_2,V_x_2] :
( ~ hBOOL(hAPP(V_A_2,V_x_2))
| ! [T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ! [V_A_2,V_x_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
| ! [T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
inference(miniscoping,[status(thm)],[f5562]) ).
fof(f5564,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5563]) ).
fof(f5565,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5563]) ).
fof(f5595,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1) = X1,
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f5604,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X3) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X3)),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f5608,plain,
! [V_B_2,V_A_2,T_b] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != V_B_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f5609,plain,
( ! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != V_B_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(miniscoping,[status(thm)],[f5608]) ).
fof(f5611,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2) != X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5609]) ).
fof(f5637,plain,
! [V_A_2,V_a_2,T_b] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f135]) ).
fof(f5638,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5637]) ).
fof(f20151,plain,
? [B_x] :
( ~ v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,B_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_U)) ),
inference(pre_NNF_transformation,[status(thm)],[f5227]) ).
fof(f20152,plain,
( ~ v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sK569_skl)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK569_skl),v_U)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK569_skl]),skolemize(B_x,sK569_skl)],[f20151]) ).
fof(f20153,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sK569_skl),v_U)),
inference(cnf_transformation,[status(thm)],[f20152]) ).
fof(f20154,plain,
~ v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sK569_skl)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
inference(cnf_transformation,[status(thm)],[f20152]) ).
fof(f20993,plain,
hBOOL(hAPP(v_U,sK569_skl)),
inference(resolution,[status(thm)],[f5564,f20153]) ).
fof(f21032,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X2,X1))
| hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2 ),
inference(resolution,[status(thm)],[f5638,f5565]) ).
fof(f21092,plain,
! [X0] : hAPP(hAPP(c_Set_Oinsert(X0),sK569_skl),v_U) = v_U,
inference(resolution,[status(thm)],[f21032,f20993]) ).
fof(f21125,plain,
! [X0,X1,X2] : hAPP(c_Set_Oimage(X0,X1,X2),v_U) = hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,sK569_skl)),hAPP(c_Set_Oimage(X0,X1,X2),v_U)),
inference(paramodulation,[status(thm)],[f21092,f5243]) ).
fof(f26842,plain,
! [X0,X1] :
( v_P(X1,X0)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(t_a,tc_HOL_Obool)),X0),X1) != X1 ),
inference(resolution,[status(thm)],[f5611,f5245]) ).
fof(f26873,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sK569_skl)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
inference(resolution,[status(thm)],[f26842,f20154]) ).
fof(f26876,plain,
hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sK569_skl)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(t_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
inference(forward_demodulation,[status(thm)],[f5604,f26873]) ).
fof(f26877,plain,
hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sK569_skl)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
inference(forward_demodulation,[status(thm)],[f5595,f26876]) ).
fof(f26878,plain,
hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U) != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
inference(forward_demodulation,[status(thm)],[f21125,f26877]) ).
fof(f26879,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f26878]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW360+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 09:52:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.80/1.07 % Drodi V4.1.1
% 28.66/4.66 % Refutation found
% 28.66/4.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 28.66/4.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 28.66/4.85 % Elapsed time: 4.462119 seconds
% 28.66/4.85 % CPU time: 29.480167 seconds
% 28.66/4.85 % Total memory used: 859.028 MB
% 28.66/4.85 % Net memory used: 846.052 MB
%------------------------------------------------------------------------------