%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET862-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 : Fri Sep 25 02:48:50 PM UTC 2026
% Result : Unsatisfiable 37.86s 11.37s
% Output : CNFRefutation 37.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 87 ( 12 unt; 0 def)
% Number of atoms : 282 ( 10 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 344 ( 149 ~; 195 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 158 ( 0 sgn 158 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f2,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f4,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
fof(f8,axiom,
! [X2,X3,X0,X1,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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
fof(f9,axiom,
! [X2,X3,X0,X1,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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
fof(f10,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f11,negated_conjecture,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f12,negated_conjecture,
c_in(v_y,v_S,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f13,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_c,tc_set(t_a))
| c_lessequals(X0,v_y,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f14,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| c_in(v_x(X0),v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f15,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| c_lessequals(X0,v_x(X0),tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f16,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| X0 != v_x(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f17,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| v_x(X0) != X0 ),
inference(reorient_equations,[],[f16]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X3,X1,X2)
| ~ c_in(X3,X0,X2)
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Zorn_Ochain__extend__1(X0,X3,X2),X0,tc_set(X2))
| c_in(c_union(c_insert(X3,c_emptyset,tc_set(X2)),X0,tc_set(X2)),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,X1,tc_set(X2))
| ~ c_in(X0,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),X0,tc_set(X2)),c_Zorn_Ochain(X3,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,X3,tc_set(X2))
| ~ c_in(X0,c_Zorn_Ochain(X3,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X1,X2),X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(X4,X5,X1)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X2,X5,X1),X2,tc_set(X1))
| ~ c_in(X4,X0,X1)
| ~ c_in(X2,c_Zorn_Omaxchain(X3,X1),tc_set(tc_set(X1)))
| ~ c_in(c_union(c_insert(X0,c_emptyset,tc_set(X1)),X2,tc_set(X1)),c_Zorn_Ochain(X3,X1),tc_set(tc_set(X1))) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(X5,X4,X1)
| ~ c_in(X5,X0,X1)
| ~ c_in(X2,c_Zorn_Omaxchain(X3,X1),tc_set(tc_set(X1)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X2,X4,X1),X4,tc_set(X1))
| ~ c_in(c_union(c_insert(X0,c_emptyset,tc_set(X1)),X2,tc_set(X1)),c_Zorn_Ochain(X3,X1),tc_set(tc_set(X1))) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,negated_conjecture,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,negated_conjecture,
c_in(v_y,v_S,tc_set(t_a)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,negated_conjecture,
! [X0: $i] :
( c_lessequals(X0,v_y,tc_set(t_a))
| ~ c_in(X0,v_c,tc_set(t_a)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,negated_conjecture,
! [X0: $i] :
( c_in(v_x(X0),v_S,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_77,negated_conjecture,
! [X0: $i] :
( c_lessequals(X0,v_x(X0),tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_78,negated_conjecture,
! [X0: $i] :
( ~ c_in(X0,v_S,tc_set(t_a))
| ( v_x(X0) != X0 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_463,plain,
( c_in(v_x(v_y),v_S,tc_set(t_a))
| ~ c_in(v_y,v_S,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_464,plain,
( c_lessequals(v_y,v_x(v_y),tc_set(t_a))
| ~ c_in(v_y,v_S,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_484,plain,
! [X0: $i] :
( c_in(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_c,tc_set(t_a))
| 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(X0,v_S,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_508,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_in(c_union(c_insert(v_x(v_y),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_y),v_S,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_484]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i] :
( ( v_x(X0) = X0 )
| ~ c_lessequals(X0,v_x(X0),tc_set(X1))
| ~ c_lessequals(v_x(X0),X0,tc_set(X1)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_521,plain,
! [X0: $i] :
( 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(X0,v_S,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,X0,t_a),X0,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_585,plain,
( ( v_x(v_y) = v_y )
| ~ c_lessequals(v_y,v_x(v_y),tc_set(t_a))
| ~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_512]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i] :
( c_in(X1,v_x(X0),t_a)
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_77,c_65]) ).
tcf(c_630,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,tc_set(t_a))
| c_in(c_union(c_insert(X1,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(X1,X0,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(X0,t_a),tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[c_68,c_75]) ).
tcf(c_663,plain,
! [X0: $i] :
( c_in(X0,v_x(v_y),t_a)
| ~ c_in(X0,v_y,t_a) ),
inference(superposition,[status(thm)],[c_74,c_624]) ).
tcf(c_681,plain,
( c_in(c_union(c_insert(v_x(v_y),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_y),v_S,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_521]) ).
tcf(c_696,plain,
! [X0: $i] :
( c_lessequals(X0,v_x(v_y),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_y),t_a),v_y,t_a) ),
inference(superposition,[status(thm)],[c_663,c_67]) ).
tcf(c_698,plain,
( ~ c_in(v_y,v_S,tc_set(t_a))
| ( v_x(v_y) != v_y ) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_723,plain,
c_lessequals(v_y,v_x(v_y),tc_set(t_a)),
inference(superposition,[status(thm)],[c_66,c_696]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X2,X3,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,tc_set(t_a))
| ~ c_in(X2,X1,t_a)
| ~ c_in(X1,X0,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(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))) ),
inference(superposition,[status(thm)],[c_630,c_70]) ).
tcf(c_1089,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X2,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_y,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[c_73,c_862]) ).
tcf(c_1105,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X2,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_y,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(global_subsumption_just,[status(thm)],[c_1089,c_72,c_1089]) ).
tcf(c_1187,plain,
! [X0: $i,X1: $i] :
( c_in(X1,v_x(X0),t_a)
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_65,c_77]) ).
tcf(c_1207,plain,
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1208,plain,
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_1820,plain,
! [X0: $i] :
( c_in(X0,v_x(v_y),t_a)
| ~ c_in(X0,v_y,t_a) ),
inference(resolution,[status(thm)],[c_1187,c_74]) ).
tcf(c_2522,plain,
( ( v_x(v_y) = v_y )
| ~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_723,c_64]) ).
tcf(c_2524,plain,
~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)),
inference(global_subsumption_just,[status(thm)],[c_2522,c_74,c_464,c_585,c_698]) ).
tcf(c_2544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(X4,X5,X2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X5,X2),X0,tc_set(X2))
| c_in(c_Zorn_Ochain__extend__1(X0,X3,X2),X0,tc_set(X2))
| ~ c_in(X4,X3,X2)
| ~ c_in(X3,X1,tc_set(X2))
| ~ c_in(X0,c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2))) ),
inference(superposition,[status(thm)],[c_68,c_70]) ).
tcf(c_2553,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X2,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[c_73,c_2544]) ).
tcf(c_2560,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X2,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(global_subsumption_just,[status(thm)],[c_2553,c_72,c_2553]) ).
tcf(c_2562,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X0,X2,t_a),X1,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,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(superposition,[status(thm)],[c_66,c_2560]) ).
tcf(c_2575,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X0,X2,t_a),X1,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_2562,c_75]) ).
tcf(c_2580,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_y,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_2575,c_67]) ).
tcf(c_2624,plain,
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_2580,c_2524]) ).
tcf(c_2809,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_y,tc_set(t_a))
| ~ c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_4445,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(X4,X5,X2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X5,X2),X0,tc_set(X2))
| c_in(c_Zorn_Ochain__extend__1(X0,X3,X2),X0,tc_set(X2))
| ~ c_in(X4,X3,X2)
| ~ c_in(X3,X1,tc_set(X2))
| ~ c_in(X0,c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2))) ),
inference(resolution,[status(thm)],[c_70,c_68]) ).
tcf(c_5404,plain,
! [X0: $i,X1: $i] :
( c_in(X1,X0,t_a)
| ~ c_in(X1,v_x(v_y),t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),X0,tc_set(t_a))
| ~ c_in(c_union(c_insert(v_x(v_y),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(instantiation,[status(thm)],[c_71]) ).
tcf(c_5405,plain,
! [X0: $i,X1: $i] :
( c_in(X0,X1,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X0,v_x(v_y),t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_union(c_insert(v_x(v_y),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(instantiation,[status(thm)],[c_70]) ).
tcf(c_5672,plain,
! [X0: $i] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),X0,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a)
| ~ c_in(c_union(c_insert(v_x(v_y),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(instantiation,[status(thm)],[c_5405]) ).
tcf(c_5717,plain,
! [X0: $i] :
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),X0,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),X0,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a)
| ~ c_in(c_union(c_insert(v_x(v_y),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(instantiation,[status(thm)],[c_5404]) ).
tcf(c_6133,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_y,tc_set(t_a))
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_6288,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(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_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a)
| ~ c_in(c_union(c_insert(v_x(v_y),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(instantiation,[status(thm)],[c_5717]) ).
tcf(c_7136,plain,
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_x(v_y),t_a)
| ~ c_in(c_union(c_insert(v_x(v_y),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(instantiation,[status(thm)],[c_5672]) ).
tcf(c_9293,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X2,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_4445,c_72]) ).
tcf(c_9826,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X2,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(global_subsumption_just,[status(thm)],[c_9293,c_2560]) ).
tcf(c_9849,plain,
! [X0: $i,X1: $i] :
( c_in(X0,X1,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| ~ c_in(X0,v_y,t_a)
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c_9826,c_1820]) ).
tcf(c_10015,plain,
c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a)),
inference(global_subsumption_just,[status(thm)],[c_9849,c_74,c_73,c_72,c_463,c_464,c_508,c_585,c_698,c_1208,c_1207,c_2624,c_6288]) ).
tcf(c_11562,plain,
! [X0: $i] :
( c_in(X0,v_x(v_y),t_a)
| ~ c_in(X0,v_y,t_a) ),
inference(superposition,[status(thm)],[c_723,c_65]) ).
tcf(c_11581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X2,X3,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,tc_set(t_a))
| ~ c_in(X2,X1,t_a)
| ~ c_in(X1,X0,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(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))) ),
inference(superposition,[status(thm)],[c_630,c_70]) ).
tcf(c_11624,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X2,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_y,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[c_73,c_11581]) ).
tcf(c_11625,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X2,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_y,tc_set(t_a))
| ~ c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(global_subsumption_just,[status(thm)],[c_11624,c_1105]) ).
tcf(c_11665,plain,
! [X0: $i] :
( c_lessequals(X0,v_x(v_y),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_y),t_a),v_y,t_a) ),
inference(superposition,[status(thm)],[c_11562,c_67]) ).
tcf(c_11666,plain,
! [X0: $i,X1: $i] :
( c_in(X0,X1,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_y,tc_set(t_a))
| ~ c_in(X0,v_y,t_a)
| ~ c_in(v_x(v_y),v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_11562,c_11625]) ).
tcf(c_11731,plain,
c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_y,tc_set(t_a)),
inference(global_subsumption_just,[status(thm)],[c_11666,c_2809,c_10015]) ).
tcf(c_11734,plain,
! [X0: $i] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),t_a) ),
inference(superposition,[status(thm)],[c_11731,c_65]) ).
tcf(c_11770,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),X0,t_a),v_y,t_a) ),
inference(superposition,[status(thm)],[c_66,c_11734]) ).
tcf(c_12172,plain,
c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a)),
inference(superposition,[status(thm)],[c_11770,c_11665]) ).
tcf(c_13470,plain,
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a))
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a)) ),
inference(instantiation,[status(thm)],[c_6133]) ).
tcf(c_13471,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13470,c_12172,c_7136,c_6288,c_1207,c_1208,c_698,c_681,c_585,c_464,c_463,c_72,c_73,c_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET862-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.40 % Computer : n005.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Thu Sep 24 12:16:53 UTC 2026
% 0.13/5.40 % CPUTime :
% 0.13/5.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.44 Running first-order theorem proving
% 0.13/5.44 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.45
% 0.13/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.45
% 0.13/5.45 % Detected problem language: tptp
% 0.13/5.47 % Proving...
% 37.86/11.37 % SZS status Started for theBenchmark.p
% 37.86/11.37 % SZS status Unsatisfiable for theBenchmark.p
% 37.86/11.37
% 37.86/11.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 37.86/11.37
% 37.86/11.37 % ------ iProver source info
% 37.86/11.37
% 37.86/11.37 % git: date: 2026-07-19 20:42:38 +0200
% 37.86/11.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 37.86/11.37 % git: non_committed_changes: false
% 37.86/11.37
% 37.86/11.37 % ------ Parsing...% successful
% 37.86/11.37
% 37.86/11.37
% 37.86/11.37 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 37.86/11.37
% 37.86/11.37 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 37.86/11.37
% 37.86/11.37 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 37.86/11.37
% 37.86/11.37 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 37.86/11.37 % ------ Proving...
% 37.86/11.37 % ------ Problem Properties
% 37.86/11.37
% 37.86/11.37 %
% 37.86/11.37 % clauses 15
% 37.86/11.37 % conjectures 7
% 37.86/11.37 % EPR 0
% 37.86/11.37 % Horn 12
% 37.86/11.37 % unary 3
% 37.86/11.37 % binary 6
% 37.86/11.37 % lits 39
% 37.86/11.37 % lits eq 2
% 37.86/11.37 % fd_pure 0
% 37.86/11.37 % fd_pseudo 0
% 37.86/11.37 % fd_cond 0
% 37.86/11.37 % fd_pseudo_cond 1
% 37.86/11.37 % AC symbols 0
% 37.86/11.37
% 37.86/11.37 % ------ Input Options Time Limit: Unbounded
% 37.86/11.37
% 37.86/11.37
% 37.86/11.37 % ------
% 37.86/11.37 % Current options:
% 37.86/11.37 % ------
% 37.86/11.37
% 37.86/11.37
% 37.86/11.37 %
% 37.86/11.37
% 37.86/11.37 % ------ Proving...
% 37.86/11.37 %
% 37.86/11.37
% 37.86/11.37 % SZS status Unsatisfiable for theBenchmark.p
% 37.86/11.37
% 37.86/11.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 37.86/11.37
% 37.86/11.37
%------------------------------------------------------------------------------