%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET852-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 02:10:49 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 7 unt; 3 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 71 ( 22 ~; 46 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_A,V_B,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_A,V_B,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_B,V_A,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0] :
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [V_A,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| ! [V_B] :
( c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| c_in(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X2,tc_set(X3)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [V_A,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| ! [V_B] :
( c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X0,tc_set(X3)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [V_A,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| ! [V_B] :
( c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Union(X2,X3),X1,tc_set(X3))
| c_lessequals(X0,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,X0,X2,X3),tc_set(X3)) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X0,v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X1,X0,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(X0,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f11,f9]) ).
fof(f17,plain,
! [X0] :
( c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f15,f16]) ).
fof(f18,definition,
( sQ0_spl
<=> c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f19,plain,
( ~ sQ0_spl
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,definition,
! [X0] :
( sQ1_spl
<=> ( c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0] :
( ~ sQ1_spl
| c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f17,f18,f21]) ).
fof(f25,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19,f8]) ).
fof(f26,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0] :
( ~ sQ1_spl
| c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(duplicate_literals_removal,[status(thm)],[f22]) ).
fof(f28,plain,
( ~ sQ1_spl
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f27,f13]) ).
fof(f29,definition,
( sQ2_spl
<=> c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f30,plain,
( ~ sQ2_spl
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,plain,
( ~ sQ1_spl
| sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f28,f29,f18,f21]) ).
fof(f33,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f7]) ).
fof(f34,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f33]) ).
fof(f35,plain,
$false,
inference(sat_refutation,[status(thm)],[f24,f26,f32,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET852-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:44:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.034745 seconds
% 0.10/0.41 % CPU time: 0.080042 seconds
% 0.10/0.41 % Total memory used: 9.469 MB
% 0.10/0.41 % Net memory used: 9.175 MB
%------------------------------------------------------------------------------