%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET863-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:10:51 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 91 ( 18 unt; 12 def)
% Number of atoms : 244 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 263 ( 110 ~; 141 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 13 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 115 ( 115 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox/benchmark/theBenchmark.p') ).
fof(f2,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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,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_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_z,V_S,T_a,V_c] :
( c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_c,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_S,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_z,V_S,T_a,V_c] :
( c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_z,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_S,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_z,V_x,T_a,V_c,V_S,V_y] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_c,tc_set(T_a))
| c_in(V_z,V_y,T_a)
| ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_x,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_z,V_x,T_a,V_c,V_S,V_y] :
( c_in(V_z,V_y,T_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_y,tc_set(T_a))
| ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_x,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
c_in(v_x,v_S,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
c_lessequals(v_y,v_x,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
c_in(v_xa,v_x,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ c_in(v_xa,v_y,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_c,tc_set(t_a))
| c_lessequals(V_U,v_y,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,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)],[f1]) ).
fof(f16,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)],[f15]) ).
fof(f17,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)],[f2]) ).
fof(f18,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( c_in(c_union(c_insert(X0,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| c_in(c_Zorn_Ochain__extend__1(X3,X0,X2),X3,tc_set(X2))
| ~ c_in(X3,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( c_in(c_union(c_insert(X0,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X3,X0,X2),X0,tc_set(X2))
| ~ c_in(X3,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [T_a,V_c,V_y] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_c,tc_set(T_a))
| ! [V_z] :
( c_in(V_z,V_y,T_a)
| ! [V_x,V_S] :
( ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_x,T_a) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X3,tc_set(X2))
| c_in(X0,X5,X2)
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [V_z,T_a,V_y] :
( c_in(V_z,V_y,T_a)
| ! [V_c] :
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_y,tc_set(T_a))
| ! [V_x,V_S] :
( ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_z,V_x,T_a) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f24,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(X0,X5,X2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X5,tc_set(X2))
| ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
c_in(v_x,v_S,tc_set(t_a)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
c_lessequals(v_y,v_x,tc_set(t_a)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
c_in(v_xa,v_x,t_a),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
~ c_in(v_xa,v_y,t_a),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
! [X0] :
( ~ c_in(X0,v_c,tc_set(t_a))
| c_lessequals(X0,v_y,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0] :
( c_in(X0,v_x,t_a)
| ~ c_in(X0,v_y,t_a) ),
inference(resolution,[status(thm)],[f16,f28]) ).
fof(f34,plain,
! [X0] :
( c_in(c_Main_OsubsetI__1(v_y,X0,t_a),v_x,t_a)
| c_lessequals(v_y,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f17,f32]) ).
fof(f36,plain,
( c_lessequals(v_y,v_x,tc_set(t_a))
| c_lessequals(v_y,v_x,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f18,f34]) ).
fof(f38,definition,
( sQ0_spl
<=> c_lessequals(v_y,v_x,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f41,plain,
sQ0_spl,
inference(split_clause,[status(thm)],[f36,f38]) ).
fof(f53,plain,
! [X0] :
( c_in(c_union(c_insert(X0,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_c,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f19,f26]) ).
fof(f58,plain,
! [X0] :
( c_lessequals(v_S,X0,tc_set(tc_set(t_a)))
| c_in(c_union(c_insert(c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),t_a),v_c,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f53,f17]) ).
fof(f59,plain,
( c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f53,f27]) ).
fof(f60,definition,
( sQ1_spl
<=> c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ1_spl
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ2_spl
<=> c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ2_spl
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f59,f60,f63]) ).
fof(f67,plain,
( ~ sQ1_spl
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f61,f31]) ).
fof(f69,plain,
! [X0] :
( ~ sQ1_spl
| c_in(X0,v_y,t_a)
| ~ c_in(X0,c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a) ),
inference(resolution,[status(thm)],[f67,f16]) ).
fof(f75,plain,
! [X0] :
( ~ sQ1_spl
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X0,t_a),v_y,t_a) ),
inference(resolution,[status(thm)],[f69,f17]) ).
fof(f77,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X0,t_a),v_x,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f75,f32]) ).
fof(f84,plain,
! [X0,X1] :
( ~ sQ2_spl
| c_in(X0,X1,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,v_x,t_a) ),
inference(resolution,[status(thm)],[f64,f24]) ).
fof(f85,plain,
! [X0,X1] :
( ~ sQ2_spl
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(X0,X1,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,v_x,t_a) ),
inference(resolution,[status(thm)],[f64,f22]) ).
fof(f88,definition,
! [X0,X1] :
( sQ4_spl
<=> ( c_in(X0,X1,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_x,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f89,plain,
! [X0,X1] :
( ~ sQ4_spl
| c_in(X0,X1,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_x,t_a) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,definition,
( sQ5_spl
<=> c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( sQ5_spl
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f84,f88,f91,f63]) ).
fof(f95,definition,
! [X0,X1] :
( sQ6_spl
<=> ( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(X0,X1,t_a)
| ~ c_in(X0,v_x,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f96,plain,
! [X0,X1] :
( ~ sQ6_spl
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(X0,X1,t_a)
| ~ c_in(X0,v_x,t_a) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f85,f95,f91,f63]) ).
fof(f99,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f25]) ).
fof(f100,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f99]) ).
fof(f114,plain,
! [X0] :
( ~ sQ6_spl
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(v_xa,X0,t_a) ),
inference(resolution,[status(thm)],[f96,f29]) ).
fof(f115,plain,
! [X0] :
( ~ sQ6_spl
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_y,tc_set(t_a))
| c_in(v_xa,X0,t_a) ),
inference(resolution,[status(thm)],[f114,f31]) ).
fof(f117,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ6_spl
| c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x,t_a)
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[f115,f89]) ).
fof(f119,definition,
( sQ7_spl
<=> c_in(v_xa,v_y,t_a) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ7_spl
| c_in(v_xa,v_y,t_a) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,definition,
! [X0] :
( sQ8_spl
<=> ( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f123,plain,
! [X0] :
( ~ sQ8_spl
| c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x,t_a) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f117,f119,f122,f95,f88]) ).
fof(f127,plain,
( ~ sQ8_spl
| ~ c_in(v_xa,v_x,t_a) ),
inference(resolution,[status(thm)],[f123,f30]) ).
fof(f129,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f127,f29]) ).
fof(f130,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f131,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f30]) ).
fof(f132,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f138,plain,
( ~ sQ1_spl
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f77,f18]) ).
fof(f139,definition,
( sQ9_spl
<=> c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( ~ sQ9_spl
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( ~ sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f138,f139,f60]) ).
fof(f148,plain,
! [X0,X1,X2] :
( c_in(X1,X2,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),X2,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),t_a)
| c_lessequals(v_S,X0,tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),t_a),v_c,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f58,f24]) ).
fof(f149,plain,
! [X0,X1,X2] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(X1,X2,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),t_a)
| c_lessequals(v_S,X0,tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),t_a),v_c,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f58,f22]) ).
fof(f152,definition,
! [X0,X1,X2] :
( sQ10_spl
<=> ( c_in(X1,X2,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),X2,tc_set(t_a))
| ~ c_in(X1,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),t_a)
| c_lessequals(v_S,X0,tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),t_a),v_c,tc_set(t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f148,f152,f91]) ).
fof(f156,definition,
! [X0,X1,X2] :
( sQ11_spl
<=> ( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(X1,X2,t_a)
| ~ c_in(X1,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),t_a)
| c_lessequals(v_S,X0,tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),t_a),v_c,tc_set(t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( ~ sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f149,f156,f91]) ).
fof(f165,plain,
! [X0] :
( ~ sQ9_spl
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(X0,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_c,c_Zorn_Ochain(X0,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f140,f20]) ).
fof(f168,plain,
( ~ sQ9_spl
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f165,f26]) ).
fof(f169,definition,
( sQ12_spl
<=> c_in(v_x,v_S,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( sQ12_spl
| ~ c_in(v_x,v_S,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( ~ sQ9_spl
| sQ2_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f168,f169,f63,f139]) ).
fof(f173,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f27]) ).
fof(f174,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f175,plain,
$false,
inference(sat_refutation,[status(thm)],[f41,f66,f94,f98,f100,f125,f130,f132,f142,f155,f159,f172,f174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET863-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:42:49 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.040231 seconds
% 0.12/0.40 % CPU time: 0.125063 seconds
% 0.12/0.40 % Total memory used: 11.859 MB
% 0.12/0.40 % Net memory used: 11.522 MB
%------------------------------------------------------------------------------