%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET844-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.12s 0.58s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 11 unt; 2 def)
% Number of atoms : 51 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 25 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| V_m != c_Zorn_Osucc(V_S,V_m,T_a)
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,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)],[f2]) ).
fof(f9,plain,
! [V_m,T_a,V_n] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ! [V_S] :
( V_m != c_Zorn_Osucc(V_S,V_m,T_a)
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| X0 != c_Zorn_Osucc(X1,X0,X2)
| ~ c_in(X3,c_Zorn_OTFin(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)],[f9]) ).
fof(f11,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f14,plain,
! [X0] :
( c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f10,f12]) ).
fof(f16,definition,
( sQ0_spl
<=> c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f18,plain,
( sQ0_spl
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,definition,
! [X0] :
( sQ1_spl
<=> ( c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f20,plain,
! [X0] :
( ~ sQ1_spl
| c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f16,f19]) ).
fof(f27,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18,f11]) ).
fof(f28,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0] :
( ~ sQ1_spl
| ~ c_lessequals(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a))))
| c_lessequals(c_Union(X0,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f20,f8]) ).
fof(f31,plain,
( ~ sQ1_spl
| c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f29,f7]) ).
fof(f32,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f13]) ).
fof(f33,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f32]) ).
fof(f34,plain,
$false,
inference(sat_refutation,[status(thm)],[f22,f28,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET844-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.54 % Computer : n018.cluster.edu
% 0.08/0.54 % Model : x86_64 x86_64
% 0.08/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.54 % Memory : 8046.5625MB
% 0.08/0.54 % OS : Linux 6.8.0-71-generic
% 0.08/0.54 % CPULimit : 300
% 0.08/0.54 % WCLimit : 300
% 0.08/0.54 % DateTime : Mon Sep 21 05:43:29 UTC 2026
% 0.08/0.55 % CPUTime :
% 0.08/0.56 % Drodi V4.1.1
% 0.12/0.58 % Refutation found
% 0.12/0.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.61 % Elapsed time: 0.055034 seconds
% 0.12/0.61 % CPU time: 0.147069 seconds
% 0.12/0.61 % Total memory used: 66.421 MB
% 0.12/0.61 % Net memory used: 65.835 MB
%------------------------------------------------------------------------------