%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET864-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 02:10:52 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 38 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_u,V_S,T_a,V_c] :
( c_Union(V_c,T_a) = V_u
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| V_U != v_x(V_U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [V_u,T_a,V_c] :
( c_Union(V_c,T_a) = V_u
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ! [V_S] :
( ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1,X2,X3] :
( c_Union(X3,X2) = X0
| ~ c_lessequals(c_Union(X3,X2),X0,tc_set(X2))
| ~ c_in(X3,c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| c_in(v_x(X0),v_S,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| c_lessequals(X0,v_x(X0),tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| X0 != v_x(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f14,plain,
c_Union(v_c,t_a) != v_x(c_Union(v_c,t_a)),
inference(resolution,[status(thm)],[f10,f13]) ).
fof(f15,plain,
c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)),
inference(resolution,[status(thm)],[f11,f10]) ).
fof(f22,plain,
c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)),
inference(resolution,[status(thm)],[f12,f10]) ).
fof(f32,plain,
! [X0] :
( c_Union(X0,t_a) = v_x(c_Union(v_c,t_a))
| ~ c_lessequals(c_Union(X0,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a))
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f8,f15]) ).
fof(f59,plain,
( c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f32,f22]) ).
fof(f60,plain,
c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a)),
inference(forward_subsumption_resolution,[status(thm)],[f59,f9]) ).
fof(f61,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f60,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET864-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:48:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.058251 seconds
% 0.10/0.43 % CPU time: 0.150546 seconds
% 0.10/0.43 % Total memory used: 41.438 MB
% 0.10/0.43 % Net memory used: 40.951 MB
%------------------------------------------------------------------------------