%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW365+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.85s 1.34s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 16 unt; 0 def)
% Number of atoms : 91 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 38 ~; 33 |; 14 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 109 ( 106 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,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/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [V_x_2,V_A_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
<=> ( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [V_A_2,T_b] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
<=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,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/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_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))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5230,hypothesis,
hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5231,conjecture,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),v_G)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5232,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),v_G)),
inference(negated_conjecture,[status(cth)],[f5231]) ).
fof(f5253,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f5269,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f5291,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)],[f20]) ).
fof(f5292,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)],[f5291]) ).
fof(f5294,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5292]) ).
fof(f5301,plain,
! [V_x_2,V_A_2,V_y_2,T_b] :
( ( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
& V_y_2 != V_x_2 )
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f5302,plain,
( ! [V_x_2,V_A_2,V_y_2] :
( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
& V_y_2 != V_x_2 )
| ! [T_b] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) )
& ! [V_x_2,V_A_2,V_y_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2
| ! [T_b] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) ) ),
inference(miniscoping,[status(thm)],[f5301]) ).
fof(f5304,plain,
! [X0,X1,X2,X3] :
( X1 != X3
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X3)) ),
inference(cnf_transformation,[status(thm)],[f5302]) ).
fof(f5332,plain,
! [V_A_2,T_b] :
( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
& ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f5333,plain,
( ! [V_A_2,T_b] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
& ! [V_A_2,T_b] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(miniscoping,[status(thm)],[f5332]) ).
fof(f5334,plain,
( ! [V_A_2,T_b] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),sK2_skl(T_b,V_A_2)),V_A_2)) )
& ! [V_A_2,T_b] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(B_x,sK2_skl(T_b,V_A_2))],[f5333]) ).
fof(f5336,plain,
! [X0,X1] :
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X0),sK2_skl(X0,X1)),X1)) ),
inference(cnf_transformation,[status(thm)],[f5334]) ).
fof(f5342,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)],[f37]) ).
fof(f5343,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)],[f5342]) ).
fof(f5444,plain,
! [V_B_2,V_A_2,V_x_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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_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))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2)) ) ),
inference(NNF_transformation,[status(thm)],[f69]) ).
fof(f5445,plain,
( ! [V_B_2,V_A_2,V_x_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))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2)) )
& ! [V_B_2,V_A_2,V_x_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))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2)) ) ),
inference(miniscoping,[status(thm)],[f5444]) ).
fof(f5448,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X3)) ),
inference(cnf_transformation,[status(thm)],[f5445]) ).
fof(f20153,plain,
hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
inference(cnf_transformation,[status(thm)],[f5230]) ).
fof(f20154,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),v_G)),
inference(cnf_transformation,[status(thm)],[f5232]) ).
fof(f20455,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),X1)),
inference(destructive_equality_resolution,[status(thm)],[f5304]) ).
fof(f21129,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1)),
inference(resolution,[status(thm)],[f5294,f5269]) ).
fof(f21247,plain,
! [X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X1),sK2_skl(X1,X0)),X0) = X0
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(resolution,[status(thm)],[f5336,f5343]) ).
fof(f21312,plain,
! [X0,X1] :
( X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK2_skl(X1,X0))) ),
inference(paramodulation,[status(thm)],[f21247,f20455]) ).
fof(f21330,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(resolution,[status(thm)],[f21312,f21129]) ).
fof(f21373,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),v_G)),
inference(paramodulation,[status(thm)],[f21330,f20154]) ).
fof(f21389,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)),
inference(paramodulation,[status(thm)],[f21330,f5253]) ).
fof(f21608,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),v_G))
| ~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)) ),
inference(resolution,[status(thm)],[f5448,f21373]) ).
fof(f21626,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),v_G)),
inference(forward_subsumption_resolution,[status(thm)],[f21608,f20153]) ).
fof(f21694,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f21626,f21389]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW365+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.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 09:49:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.79/1.03 % Drodi V4.1.1
% 0.85/1.34 % Refutation found
% 0.85/1.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.85/1.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.88/1.44 % Elapsed time: 1.075170 seconds
% 0.88/1.44 % CPU time: 3.092476 seconds
% 0.88/1.44 % Total memory used: 680.072 MB
% 0.88/1.44 % Net memory used: 673.746 MB
%------------------------------------------------------------------------------