%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET865-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.18s 0.51s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 55 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 30 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(V_U,t_a),v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,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(f3,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(f4,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(f5,axiom,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_S,T_a] : c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,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(f8,axiom,
! [V_S,T_a] : c_lessequals(c_Zorn_Omaxchain(V_S,T_a),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(X0,t_a),v_S,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,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)],[f2]) ).
fof(f11,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)],[f3]) ).
fof(f12,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| X0 != v_x(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [V_c,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ! [V_A] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] : c_in(c_Zorn_OHausdorff__1(X0,X1),c_Zorn_Omaxchain(X0,X1),tc_set(tc_set(X1))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,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)],[f7]) ).
fof(f17,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)],[f16]) ).
fof(f18,plain,
! [X0,X1] : c_lessequals(c_Zorn_Omaxchain(X0,X1),c_Zorn_Ochain(X0,X1),tc_set(tc_set(tc_set(X1)))),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0,X1,X2] :
( c_in(c_Zorn_OHausdorff__1(X0,X1),X2,tc_set(tc_set(X1)))
| ~ c_lessequals(c_Zorn_Omaxchain(X0,X1),X2,tc_set(tc_set(tc_set(X1)))) ),
inference(resolution,[status(thm)],[f15,f14]) ).
fof(f21,plain,
! [X0,X1] : c_in(c_Zorn_OHausdorff__1(X0,X1),c_Zorn_Ochain(X0,X1),tc_set(tc_set(X1))),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f22,plain,
c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)),
inference(resolution,[status(thm)],[f21,f9]) ).
fof(f25,plain,
c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),v_S,tc_set(t_a)),
inference(resolution,[status(thm)],[f22,f10]) ).
fof(f26,plain,
c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),tc_set(t_a)),
inference(resolution,[status(thm)],[f22,f11]) ).
fof(f27,plain,
c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) != v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),
inference(resolution,[status(thm)],[f22,f12]) ).
fof(f33,plain,
! [X0] :
( c_Union(X0,t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a))
| ~ c_lessequals(c_Union(X0,t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),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)],[f25,f17]) ).
fof(f67,plain,
( c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a))
| ~ c_in(c_Zorn_OHausdorff__1(v_S,t_a),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f33,f26]) ).
fof(f68,plain,
c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),
inference(forward_subsumption_resolution,[status(thm)],[f67,f15]) ).
fof(f69,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f68,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET865-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 % Computer : n007.cluster.edu
% 0.18/0.48 % Model : x86_64 x86_64
% 0.18/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.48 % Memory : 8046.5625MB
% 0.18/0.48 % OS : Linux 6.8.0-71-generic
% 0.18/0.48 % CPULimit : 300
% 0.18/0.48 % WCLimit : 300
% 0.18/0.48 % DateTime : Mon Sep 21 05:40:36 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 0.18/0.51 % Refutation found
% 0.18/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.57 % Elapsed time: 0.082052 seconds
% 0.22/0.57 % CPU time: 0.115050 seconds
% 0.22/0.57 % Total memory used: 5.827 MB
% 0.22/0.57 % Net memory used: 5.809 MB
%------------------------------------------------------------------------------