%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW361+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 : n008.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 12.58s 8.14s
% Output : CNFRefutation 13.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 17 unt; 2 def)
% Number of atoms : 103 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 48 ~; 37 |; 10 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 113 ( 110 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,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(f25,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_b_2 = hAPP(V_f_2,V_x_2)
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,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(f60,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f100,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f5226,hypothesis,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5227,conjecture,
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,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5228,negated_conjecture,
~ 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,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
inference(negated_conjecture,[status(cth)],[f5227]) ).
fof(f5247,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)],[f8]) ).
fof(f5282,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)],[f17]) ).
fof(f5283,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)],[f5282]) ).
fof(f5284,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5283]) ).
fof(f5285,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5283]) ).
fof(f5303,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)],[f25]) ).
fof(f5304,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)],[f5303]) ).
fof(f5305,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))],[f5304]) ).
fof(f5307,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)],[f5305]) ).
fof(f5329,plain,
! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| V_b_2 != hAPP(V_f_2,V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f5330,plain,
! [V_A_2,V_x_2,T_b] :
( ! [V_f_2,V_b_2] :
( ! [T_c] : hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| V_b_2 != hAPP(V_f_2,V_x_2) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(miniscoping,[status(thm)],[f5329]) ).
fof(f5331,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),hAPP(c_Set_Oimage(X0,X5,X4),X2)))
| X3 != hAPP(X4,X1)
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5330]) ).
fof(f5377,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)],[f49]) ).
fof(f5378,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)],[f5377]) ).
fof(f5412,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)],[f60]) ).
fof(f5540,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)],[f100]) ).
fof(f5541,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)],[f5540]) ).
fof(f5544,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)],[f5541]) ).
fof(f20147,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
inference(cnf_transformation,[status(thm)],[f5226]) ).
fof(f20148,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,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
inference(cnf_transformation,[status(thm)],[f5228]) ).
fof(f20484,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(X3),hAPP(X4,X1)),hAPP(c_Set_Oimage(X0,X3,X4),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f5331]) ).
fof(f22645,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1)),
inference(resolution,[status(thm)],[f5285,f5247]) ).
fof(f22990,plain,
! [X0,X1,X2] : ~ hBOOL(hAPP(hAPP(c_member(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(resolution,[status(thm)],[f22645,f5284]) ).
fof(f23040,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)],[f22990,f5307]) ).
fof(f23440,plain,
! [X0] : ~ 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,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(paramodulation,[status(thm)],[f23040,f20148]) ).
fof(f24682,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)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(resolution,[status(thm)],[f5378,f23440]) ).
fof(f27192,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))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(resolution,[status(thm)],[f5544,f24682]) ).
fof(f27193,definition,
( sQ189_spl
<=> hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f27195,plain,
( sQ189_spl
| ~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(component_clause,[status(thm)],[f27193]) ).
fof(f27196,definition,
! [X0] :
( sQ190_spl
<=> ~ 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))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f27197,plain,
! [X0] :
( ~ sQ190_spl
| ~ 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))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(component_clause,[status(thm)],[f27196]) ).
fof(f27199,plain,
( sQ190_spl
| ~ sQ189_spl ),
inference(split_clause,[status(thm)],[f27192,f27193,f27196]) ).
fof(f27783,plain,
( sQ189_spl
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)) ),
inference(resolution,[status(thm)],[f27195,f20484]) ).
fof(f27820,plain,
( sQ189_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27783,f20147]) ).
fof(f27821,plain,
sQ189_spl,
inference(contradiction_clause,[status(thm)],[f27820]) ).
fof(f30511,plain,
( ~ sQ190_spl
| $false ),
inference(resolution,[status(thm)],[f27197,f5412]) ).
fof(f30548,plain,
~ sQ190_spl,
inference(contradiction_clause,[status(thm)],[f30511]) ).
fof(f30549,plain,
$false,
inference(sat_refutation,[status(thm)],[f27199,f27821,f30548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW361+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.42 % Computer : n008.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Mon Sep 21 09:49:59 UTC 2026
% 0.16/5.42 % CPUTime :
% 1.23/6.54 % Drodi V4.1.1
% 12.58/8.14 % Refutation found
% 12.58/8.14 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.58/8.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.80/8.33 % Elapsed time: 2.878119 seconds
% 9.80/8.33 % CPU time: 13.878578 seconds
% 9.80/8.33 % Total memory used: 751.113 MB
% 9.80/8.33 % Net memory used: 742.879 MB
%------------------------------------------------------------------------------