%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW367+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 : 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 03:07:44 PM UTC 2026
% Result : Theorem 5.62s 6.81s
% Output : CNFRefutation 6.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 44 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 45 ( 21 ~; 16 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
( V_b_2 = hAPP(V_f_2,V_x_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,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(f5225,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5228,hypothesis,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5230,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)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5231,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)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(negated_conjecture,[status(cth)],[f5230]) ).
fof(f5250,plain,
! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| V_b_2 != hAPP(V_f_2,V_x_2) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f5251,plain,
! [V_x_2,V_f_2,V_b_2] :
( ! [V_A_2,T_c] :
( ! [T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) )
| V_b_2 != hAPP(V_f_2,V_x_2) ),
inference(miniscoping,[status(thm)],[f5250]) ).
fof(f5252,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X0),hAPP(c_Set_Oimage(X3,X5,X1),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X4))
| X0 != hAPP(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5251]) ).
fof(f5396,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)],[f53]) ).
fof(f5397,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)],[f5396]) ).
fof(f5400,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)],[f5397]) ).
fof(f20146,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(cnf_transformation,[status(thm)],[f5225]) ).
fof(f20149,plain,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
inference(cnf_transformation,[status(thm)],[f5228]) ).
fof(f20151,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)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(cnf_transformation,[status(thm)],[f5231]) ).
fof(f20448,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)],[f5252]) ).
fof(f21825,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),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)],[f5400,f20151]) ).
fof(f21846,plain,
~ 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(forward_subsumption_resolution,[status(thm)],[f21825,f20146]) ).
fof(f21847,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
inference(resolution,[status(thm)],[f21846,f20448]) ).
fof(f21849,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f21847,f20149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW367+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 09:49:40 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.78/6.06 % Drodi V4.1.1
% 5.62/6.81 % Refutation found
% 5.62/6.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.62/6.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.79/6.97 % Elapsed time: 1.563355 seconds
% 2.79/6.97 % CPU time: 6.651316 seconds
% 2.79/6.97 % Total memory used: 700.874 MB
% 2.79/6.97 % Net memory used: 694.393 MB
%------------------------------------------------------------------------------