%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET847-1 : 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 02:10:47 PM UTC 2026
% Result : Unsatisfiable 2.50s 0.83s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 52 ( 13 unt; 4 def)
% Number of atoms : 99 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 43 ~; 43 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 72 ( 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f159,axiom,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a)
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f174,axiom,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f299,axiom,
! [V_A,T_a] : c_lessequals(c_emptyset,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f300,axiom,
! [V_A,V_B,T_a] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_less(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f302,axiom,
! [V_A,V_B,T_a] :
( V_A = V_B
| c_less(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f307,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f310,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1359,axiom,
! [V_Y,V_S,T_a] :
( c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1360,axiom,
! [V_c,V_S,T_a] :
( c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1362,axiom,
! [V_S,T_a] :
( c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)) = c_Zorn_Osucc(V_S,c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),T_a)
| ~ c_in(c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1363,axiom,
! [V_c,V_S,T_a] :
( c_Zorn_Osucc(V_S,V_c,T_a) != V_c
| ~ c_in(V_c,c_minus(c_Zorn_Ochain(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1364,negated_conjecture,
! [V_U] : ~ c_in(V_U,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1580,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_minus(X1,X3,tc_set(X2)),X2)
| c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f1604,plain,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f1767,plain,
! [X0,X1] : c_lessequals(c_emptyset,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f1768,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_less(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f300]) ).
fof(f1770,plain,
! [V_A,V_B] :
( V_A = V_B
| ! [T_a] :
( c_less(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f302]) ).
fof(f1771,plain,
! [X0,X1,X2] :
( X0 = X1
| c_less(X0,X1,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f1770]) ).
fof(f1779,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f1783,plain,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f310]) ).
fof(f2841,plain,
! [X0,X1,X2] :
( c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))) ),
inference(cnf_transformation,[status(thm)],[f1359]) ).
fof(f2842,plain,
! [X0,X1,X2] :
( c_in(X0,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(thm)],[f1360]) ).
fof(f2844,plain,
! [X0,X1] :
( c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)) = c_Zorn_Osucc(X0,c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),X1)
| ~ c_in(c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),c_Zorn_OTFin(X0,X1),tc_set(tc_set(X1))) ),
inference(cnf_transformation,[status(thm)],[f1362]) ).
fof(f2845,plain,
! [X0,X1,X2] :
( c_Zorn_Osucc(X1,X0,X2) != X0
| ~ c_in(X0,c_minus(c_Zorn_Ochain(X1,X2),c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(tc_set(X2)))),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(thm)],[f1363]) ).
fof(f2846,plain,
! [X0] : ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1364]) ).
fof(f4770,plain,
! [X0,X1] :
( c_emptyset = X0
| c_less(c_emptyset,X0,tc_set(X1)) ),
inference(resolution,[status(thm)],[f1771,f1767]) ).
fof(f4781,plain,
! [X0,X1] :
( ~ c_lessequals(X0,c_emptyset,tc_set(X1))
| c_emptyset = X0 ),
inference(resolution,[status(thm)],[f4770,f1768]) ).
fof(f4819,plain,
! [X0] : c_lessequals(c_Zorn_Omaxchain(v_S,t_a),X0,tc_set(tc_set(tc_set(t_a)))),
inference(resolution,[status(thm)],[f1779,f2846]) ).
fof(f4852,plain,
c_emptyset = c_Zorn_Omaxchain(v_S,t_a),
inference(resolution,[status(thm)],[f4819,f4781]) ).
fof(f6345,plain,
! [X0,X1] :
( ~ c_in(c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),c_minus(c_Zorn_Ochain(X0,X1),c_Zorn_Omaxchain(X0,X1),tc_set(tc_set(tc_set(X1)))),tc_set(tc_set(X1)))
| ~ c_in(c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),c_Zorn_OTFin(X0,X1),tc_set(tc_set(X1))) ),
inference(resolution,[status(thm)],[f2844,f2845]) ).
fof(f6351,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_minus(c_Zorn_Ochain(v_S,t_a),c_emptyset,tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a)))
| ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(paramodulation,[status(thm)],[f4852,f6345]) ).
fof(f6353,definition,
( sQ52_spl
<=> c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f6354,plain,
( ~ sQ52_spl
| c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f6353]) ).
fof(f6355,plain,
( sQ52_spl
| ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f6353]) ).
fof(f6356,definition,
( sQ53_spl
<=> c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_minus(c_Zorn_Ochain(v_S,t_a),c_emptyset,tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f6358,plain,
( sQ53_spl
| ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_minus(c_Zorn_Ochain(v_S,t_a),c_emptyset,tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f6356]) ).
fof(f6359,plain,
( ~ sQ53_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f6351,f6353,f6356]) ).
fof(f6360,plain,
( sQ52_spl
| ~ c_lessequals(c_Zorn_OTFin(v_S,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))) ),
inference(resolution,[status(thm)],[f6355,f2841]) ).
fof(f6361,plain,
( sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6360,f1783]) ).
fof(f6362,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f6361]) ).
fof(f6363,plain,
( ~ sQ52_spl
| c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f6354,f2842]) ).
fof(f6380,plain,
( sQ53_spl
| c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_emptyset,tc_set(tc_set(t_a)))
| ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f6358,f1580]) ).
fof(f6381,definition,
( sQ58_spl
<=> c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f6383,plain,
( sQ58_spl
| ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f6381]) ).
fof(f6384,definition,
( sQ59_spl
<=> c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_emptyset,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f6385,plain,
( ~ sQ59_spl
| c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_emptyset,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f6384]) ).
fof(f6387,plain,
( sQ53_spl
| sQ59_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f6380,f6381,f6384,f6356]) ).
fof(f6388,plain,
( sQ58_spl
| ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6383,f6363]) ).
fof(f6389,plain,
( sQ58_spl
| ~ sQ52_spl ),
inference(contradiction_clause,[status(thm)],[f6388]) ).
fof(f6390,plain,
( ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6385,f1604]) ).
fof(f6391,plain,
~ sQ59_spl,
inference(contradiction_clause,[status(thm)],[f6390]) ).
fof(f6392,plain,
$false,
inference(sat_refutation,[status(thm)],[f6359,f6362,f6387,f6389,f6391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET847-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 05:39:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.42 % Drodi V4.1.1
% 2.50/0.83 % Refutation found
% 2.50/0.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.50/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.50/0.85 % Elapsed time: 0.478743 seconds
% 2.50/0.85 % CPU time: 3.275317 seconds
% 2.50/0.85 % Total memory used: 217.820 MB
% 2.50/0.85 % Net memory used: 214.520 MB
%------------------------------------------------------------------------------