%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET863-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 2.35s 1.18s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 18
% Syntax : Number of formulae : 82 ( 26 unt; 4 def)
% Number of atoms : 370 ( 4 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 255 ( 109 ~; 146 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 141 ( 0 sgn 141 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f2,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f3,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f4,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/sandbox/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
fof(f5,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/sandbox/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
fof(f6,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/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
fof(f7,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/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
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',cls_conjecture_0) ).
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',cls_conjecture_1) ).
fof(f10,negated_conjecture,
c_in(v_x,v_S,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f11,negated_conjecture,
c_lessequals(v_y,v_x,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f12,negated_conjecture,
c_in(v_xa,v_x,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f13,negated_conjecture,
~ c_in(v_xa,v_y,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f14,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_c,tc_set(t_a))
| c_lessequals(X0,v_y,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
tcf(c_63,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,[],[f1]) ).
tcf(c_64,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,[],[f2]) ).
tcf(c_65,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,[],[f3]) ).
tcf(c_66,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,[],[f4]) ).
tcf(c_67,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,[],[f5]) ).
tcf(c_68,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,[],[f6]) ).
tcf(c_69,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,[],[f7]) ).
tcf(c_70,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,negated_conjecture,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,negated_conjecture,
c_in(v_x,v_S,tc_set(t_a)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,negated_conjecture,
c_lessequals(v_y,v_x,tc_set(t_a)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,negated_conjecture,
c_in(v_xa,v_x,t_a),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,negated_conjecture,
~ c_in(v_xa,v_y,t_a),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,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,[],[f14]) ).
tcf(c_316,definition,
iPr_def_10 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_317,definition,
iPr_def_11 = c_Zorn_Ochain(v_S,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_318,definition,
iPr_def_12 = tc_set(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_319,definition,
iPr_def_13 = c_Zorn_Omaxchain(v_S,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_320,negated_conjecture,
! [X0: $i] :
( c_lessequals(X0,v_y,iPr_def_10)
| ~ c_in(X0,v_c,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_76,c_316]) ).
tcf(c_321,negated_conjecture,
~ c_in(v_xa,v_y,t_a),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_322,negated_conjecture,
c_in(v_xa,v_x,t_a),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_323,negated_conjecture,
c_lessequals(v_y,v_x,iPr_def_10),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_324,negated_conjecture,
c_in(v_x,v_S,iPr_def_10),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_325,negated_conjecture,
c_in(v_c,iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_71,c_318,c_317]) ).
tcf(c_326,negated_conjecture,
c_in(v_c,iPr_def_13,iPr_def_12),
inference(demodulation,[status(thm)],[c_70,c_319]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,X2,t_a)
| ~ c_lessequals(X1,X2,iPr_def_10)
| ~ c_in(X0,X1,t_a) ),
inference(superposition,[status(thm)],[c_316,c_63]) ).
tcf(c_653,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_lessequals(X0,X1,iPr_def_10) ),
inference(superposition,[status(thm)],[c_64,c_639]) ).
tcf(c_657,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,iPr_def_10)
| c_in(c_Main_OsubsetI__1(X0,X2,t_a),X1,t_a)
| ~ c_lessequals(X0,X1,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_653,c_316]) ).
tcf(c_694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X3,iPr_def_10)
| c_in(c_Main_OsubsetI__1(X0,X3,t_a),X2,t_a)
| ~ c_lessequals(X1,X2,iPr_def_10)
| ~ c_lessequals(X0,X1,iPr_def_10) ),
inference(superposition,[status(thm)],[c_657,c_639]) ).
tcf(c_761,plain,
! [X0: $i,X1: $i] :
( c_in(c_Zorn_Ochain__extend__1(X0,X1,t_a),X0,tc_set(t_a))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),iPr_def_11,tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[c_317,c_66]) ).
tcf(c_774,plain,
! [X0: $i,X1: $i] :
( c_in(c_Zorn_Ochain__extend__1(X0,X1,t_a),X0,iPr_def_10)
| c_in(c_union(c_insert(X1,c_emptyset,iPr_def_10),X0,iPr_def_10),iPr_def_11,iPr_def_12)
| ~ c_in(X1,v_S,iPr_def_10)
| ~ c_in(X0,iPr_def_11,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_761,c_316,c_317,c_318]) ).
tcf(c_792,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_union(c_insert(X2,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),c_Zorn_Ochain(X1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,X1,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X2,t_a),X2,iPr_def_10)
| ~ c_in(X0,c_Zorn_Ochain(X1,t_a),tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[c_316,c_67]) ).
tcf(c_799,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_union(c_insert(X1,c_emptyset,iPr_def_10),X0,iPr_def_10),c_Zorn_Ochain(X2,t_a),iPr_def_12)
| ~ c_in(X1,X2,iPr_def_10)
| ~ c_in(X0,c_Zorn_Ochain(X2,t_a),iPr_def_12)
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X1,t_a),X1,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_792,c_316,c_318]) ).
tcf(c_821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X2,X3,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X1,tc_set(t_a))
| ~ c_in(X2,X0,t_a)
| ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_union(c_insert(X0,c_emptyset,tc_set(t_a)),X1,tc_set(t_a)),iPr_def_11,tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[c_317,c_68]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X2,X3,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X1,iPr_def_10)
| ~ c_in(X1,iPr_def_13,iPr_def_12)
| ~ c_in(X2,X0,t_a)
| ~ c_in(c_union(c_insert(X0,c_emptyset,iPr_def_10),X1,iPr_def_10),iPr_def_11,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_821,c_316,c_318,c_319]) ).
tcf(c_864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X3,X2,t_a)
| ~ c_in(X3,X0,t_a)
| ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X1,X2,t_a),X2,tc_set(t_a))
| ~ c_in(c_union(c_insert(X0,c_emptyset,tc_set(t_a)),X1,tc_set(t_a)),iPr_def_11,tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[c_317,c_69]) ).
tcf(c_879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X3,X2,t_a)
| ~ c_in(X1,iPr_def_13,iPr_def_12)
| ~ c_in(X3,X0,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X1,X2,t_a),X2,iPr_def_10)
| ~ c_in(c_union(c_insert(X0,c_emptyset,iPr_def_10),X1,iPr_def_10),iPr_def_11,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_864,c_316,c_318,c_319]) ).
tcf(c_1196,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_y,iPr_def_10)
| c_in(c_union(c_insert(X0,c_emptyset,iPr_def_10),v_c,iPr_def_10),iPr_def_11,iPr_def_12)
| ~ c_in(v_c,iPr_def_11,iPr_def_12)
| ~ c_in(X0,v_S,iPr_def_10) ),
inference(superposition,[status(thm)],[c_774,c_320]) ).
tcf(c_1198,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,X0,t_a),v_y,iPr_def_10)
| c_in(c_union(c_insert(X0,c_emptyset,iPr_def_10),v_c,iPr_def_10),iPr_def_11,iPr_def_12)
| ~ c_in(X0,v_S,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1196,c_325]) ).
tcf(c_1509,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,X2,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,iPr_def_10)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,iPr_def_10)
| ~ c_in(v_c,iPr_def_13,iPr_def_12)
| ~ c_in(X1,v_S,iPr_def_10)
| ~ c_in(X0,X1,t_a) ),
inference(superposition,[status(thm)],[c_1198,c_836]) ).
tcf(c_1510,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,X2,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,iPr_def_10)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,iPr_def_10)
| ~ c_in(X1,v_S,iPr_def_10)
| ~ c_in(X0,X1,t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1509,c_326]) ).
tcf(c_1615,plain,
! [X0: $i] :
( c_in(v_xa,X0,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,iPr_def_10)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,iPr_def_10)
| ~ c_in(v_x,v_S,iPr_def_10) ),
inference(superposition,[status(thm)],[c_322,c_1510]) ).
tcf(c_1625,plain,
! [X0: $i] :
( c_in(v_xa,X0,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,iPr_def_10)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1615,c_324]) ).
tcf(c_1741,plain,
! [X0: $i] :
( c_in(v_xa,X0,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,iPr_def_10)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_y,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1625,c_320]) ).
tcf(c_4205,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X0,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X2,t_a),v_y,iPr_def_10)
| ~ c_in(v_c,iPr_def_13,iPr_def_12)
| ~ c_in(X2,v_S,iPr_def_10)
| ~ c_in(X1,X2,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1198,c_879]) ).
tcf(c_4206,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X1,X0,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X2,t_a),v_y,iPr_def_10)
| ~ c_in(X2,v_S,iPr_def_10)
| ~ c_in(X1,X2,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4205,c_326]) ).
tcf(c_4474,plain,
! [X0: $i,X1: $i] :
( c_in(v_xa,v_y,t_a)
| c_in(X0,v_y,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,iPr_def_10)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,iPr_def_10)
| ~ c_in(X1,v_S,iPr_def_10)
| ~ c_in(X0,X1,t_a) ),
inference(superposition,[status(thm)],[c_1741,c_4206]) ).
tcf(c_4478,plain,
! [X0: $i,X1: $i] :
( c_in(X0,v_y,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,iPr_def_10)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_y,iPr_def_10)
| ~ c_in(X1,v_S,iPr_def_10)
| ~ c_in(X0,X1,t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4474,c_321]) ).
tcf(c_4604,plain,
( c_in(v_xa,v_y,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,iPr_def_10)
| ~ c_in(v_x,v_S,iPr_def_10) ),
inference(superposition,[status(thm)],[c_322,c_4478]) ).
tcf(c_4627,plain,
c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_4604,c_321,c_324]) ).
tcf(c_4631,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X1,iPr_def_10)
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X1,t_a),X0,t_a)
| ~ c_lessequals(v_y,X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4627,c_694]) ).
tcf(c_4858,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X0,iPr_def_10)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X0,tc_set(t_a))
| ~ c_lessequals(v_y,X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4631,c_65]) ).
tcf(c_4861,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X0,iPr_def_10)
| ~ c_lessequals(v_y,X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_4858,c_316]) ).
tcf(c_4884,plain,
! [X0: $i] :
( c_in(c_union(c_insert(v_x,c_emptyset,iPr_def_10),v_c,iPr_def_10),c_Zorn_Ochain(X0,t_a),iPr_def_12)
| ~ c_lessequals(v_y,v_x,iPr_def_10)
| ~ c_in(v_x,X0,iPr_def_10)
| ~ c_in(v_c,c_Zorn_Ochain(X0,t_a),iPr_def_12) ),
inference(superposition,[status(thm)],[c_4861,c_799]) ).
tcf(c_4889,plain,
! [X0: $i] :
( c_in(c_union(c_insert(v_x,c_emptyset,iPr_def_10),v_c,iPr_def_10),c_Zorn_Ochain(X0,t_a),iPr_def_12)
| ~ c_in(v_x,X0,iPr_def_10)
| ~ c_in(v_c,c_Zorn_Ochain(X0,t_a),iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4884,c_323]) ).
tcf(c_4900,plain,
( c_in(c_union(c_insert(v_x,c_emptyset,iPr_def_10),v_c,iPr_def_10),iPr_def_11,iPr_def_12)
| ~ c_in(v_x,v_S,iPr_def_10)
| ~ c_in(v_c,c_Zorn_Ochain(v_S,t_a),iPr_def_12) ),
inference(superposition,[status(thm)],[c_317,c_4889]) ).
tcf(c_4903,plain,
( c_in(c_union(c_insert(v_x,c_emptyset,iPr_def_10),v_c,iPr_def_10),iPr_def_11,iPr_def_12)
| ~ c_in(v_x,v_S,iPr_def_10)
| ~ c_in(v_c,iPr_def_11,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_4900,c_317]) ).
tcf(c_4904,plain,
c_in(c_union(c_insert(v_x,c_emptyset,iPr_def_10),v_c,iPr_def_10),iPr_def_11,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_4903,c_324,c_325]) ).
tcf(c_4933,plain,
! [X0: $i,X1: $i] :
( c_in(X1,X0,t_a)
| ~ c_in(v_c,iPr_def_13,iPr_def_12)
| ~ c_in(X1,v_x,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4904,c_879]) ).
tcf(c_4934,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,iPr_def_10)
| ~ c_in(v_c,iPr_def_13,iPr_def_12)
| ~ c_in(X0,v_x,t_a) ),
inference(superposition,[status(thm)],[c_4904,c_836]) ).
tcf(c_4935,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,iPr_def_10)
| ~ c_in(X0,v_x,t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4934,c_326]) ).
tcf(c_4939,plain,
! [X0: $i,X1: $i] :
( c_in(X1,X0,t_a)
| ~ c_in(X1,v_x,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4933,c_326]) ).
tcf(c_4975,plain,
! [X0: $i] :
( c_in(v_xa,X0,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,iPr_def_10) ),
inference(superposition,[status(thm)],[c_322,c_4935]) ).
tcf(c_5117,plain,
! [X0: $i] :
( c_in(v_xa,X0,t_a)
| c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_y,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4975,c_320]) ).
tcf(c_5200,plain,
! [X0: $i] :
( c_in(v_xa,v_y,t_a)
| c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x,t_a) ),
inference(superposition,[status(thm)],[c_5117,c_4939]) ).
tcf(c_5203,plain,
! [X0: $i] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,v_x,t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5200,c_321]) ).
tcf(c_5243,plain,
c_in(v_xa,v_y,t_a),
inference(superposition,[status(thm)],[c_322,c_5203]) ).
tcf(c_5256,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5243,c_321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET863-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 12:16:51 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.35/1.18 % SZS status Started for theBenchmark.p
% 2.35/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 2.35/1.18
% 2.35/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.35/1.18
% 2.35/1.18 % ------ iProver source info
% 2.35/1.18
% 2.35/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.35/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.35/1.18 % git: non_committed_changes: false
% 2.35/1.18
% 2.35/1.18 % ------ Parsing...% successful
% 2.35/1.18
% 2.35/1.18
% 2.35/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.35/1.18
% 2.35/1.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.35/1.18
% 2.35/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.35/1.18
% 2.35/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.35/1.18 % ------ Proving...
% 2.35/1.18 % ------ Problem Properties
% 2.35/1.18
% 2.35/1.18 %
% 2.35/1.18 % clauses 18
% 2.35/1.18 % conjectures 7
% 2.35/1.18 % EPR 7
% 2.35/1.18 % Horn 15
% 2.35/1.18 % unary 10
% 2.35/1.18 % binary 3
% 2.35/1.18 % lits 37
% 2.35/1.18 % lits eq 4
% 2.35/1.18 % fd_pure 0
% 2.35/1.18 % fd_pseudo 0
% 2.35/1.18 % fd_cond 0
% 2.35/1.18 % fd_pseudo_cond 0
% 2.35/1.18 % AC symbols 0
% 2.35/1.18
% 2.35/1.18 % ------ Schedule dynamic 5 is on
% 2.35/1.18
% 2.35/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.35/1.18
% 2.35/1.18
% 2.35/1.18 % ------
% 2.35/1.18 % Current options:
% 2.35/1.18 % ------
% 2.35/1.18
% 2.35/1.18
% 2.35/1.18 %
% 2.35/1.18
% 2.35/1.18 % ------ Proving...
% 2.35/1.18 %
% 2.35/1.18
% 2.35/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 2.35/1.18
% 2.35/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.35/1.18
% 2.35/1.18
%------------------------------------------------------------------------------