%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET862-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 02:44:10 PM UTC 2026
% Result : Unsatisfiable 35.27s 4.98s
% Output : Proof 35.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 15
% Syntax : Number of formulae : 101 ( 15 unt; 0 def)
% Number of atoms : 277 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 285 ( 109 ~; 176 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% 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 : 191 ( 0 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
( 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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
fof(f7_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( 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(esa)],[f7_sk]) ).
cnf(f2,axiom,
( 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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f2_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p112,plain,
( c_lessequals(X3,X5,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X3,X5,X2),X4,X2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X0,X4,X2),X4,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(X0,c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2))) ),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(f8,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(f8_nnf,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(p812,plain,
( c_lessequals(X0,X2,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X0,X2,t_a),X1,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),X1,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))) ),
inference(resolution,[status(thm)],[p112,c8]) ).
cnf(f4,axiom,
( 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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
fof(f4_nnf,plain,
! [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)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [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)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( 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(esa)],[f4_sk]) ).
cnf(f12,negated_conjecture,
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f12_nnf,plain,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_in(v_x(V_U),v_S,tc_set(t_a)) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( ~ c_in(X0,v_S,tc_set(t_a))
| c_in(v_x(X0),v_S,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(f10,negated_conjecture,
c_in(v_y,v_S,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f10_nnf,plain,
c_in(v_y,v_S,tc_set(t_a)),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
c_in(v_y,v_S,tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(p15,plain,
c_in(v_x(v_y),v_S,tc_set(t_a)),
inference(resolution,[status(thm)],[c12,c10]) ).
cnf(p53,plain,
( c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(X0,v_x(v_y),t_a),X0,tc_set(t_a))
| ~ c_in(X0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c4,p15]) ).
cnf(f9,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(f9_nnf,plain,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(p243,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(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p53,c9]) ).
cnf(p1896,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_lessequals(v_x(v_y),X1,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),X1,t_a),X0,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p812,p243]) ).
cnf(f6,axiom,
( 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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
fof(f6_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( 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(esa)],[f6_sk]) ).
cnf(p97,plain,
( c_lessequals(X3,X4,tc_set(X2))
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X5,X2),X0,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X3,X4,X2),X5,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(X0,c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2))) ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(p661,plain,
( c_lessequals(X0,X1,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X0,X1,t_a),X2,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))) ),
inference(resolution,[status(thm)],[p97,c8]) ).
cnf(p1528,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_lessequals(v_x(v_y),X0,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),X0,t_a),X1,t_a) ),
inference(resolution,[status(thm)],[p661,p243]) ).
cnf(f3,axiom,
( 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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f3_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p1637,plain,
( c_lessequals(v_x(v_y),X0,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_lessequals(v_x(v_y),X0,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p1528,c3]) ).
cnf(p1648,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_lessequals(v_x(v_y),X0,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),v_c,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p1637]) ).
cnf(f11,negated_conjecture,
( ~ c_in(V_U,v_c,tc_set(t_a))
| c_lessequals(V_U,v_y,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f11_nnf,plain,
! [V_U] :
( ~ c_in(V_U,v_c,tc_set(t_a))
| c_lessequals(V_U,v_y,tc_set(t_a)) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [V_U] :
( ~ c_in(V_U,v_c,tc_set(t_a))
| c_lessequals(V_U,v_y,tc_set(t_a)) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ c_in(X0,v_c,tc_set(t_a))
| c_lessequals(X0,v_y,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p1649,plain,
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,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_lessequals(v_x(v_y),X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p1648,c11]) ).
cnf(p1903,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_lessequals(v_x(v_y),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_lessequals(v_x(v_y),X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),X0,t_a),v_y,t_a) ),
inference(resolution,[status(thm)],[p1896,p1649]) ).
cnf(p5372,plain,
( c_lessequals(v_x(v_y),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_lessequals(v_x(v_y),X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),X0,t_a),v_y,t_a) ),
inference(factoring,[status(thm)],[p1903]) ).
cnf(p5410,plain,
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| c_lessequals(v_x(v_y),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_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5372,c3]) ).
cnf(p5425,plain,
( c_lessequals(v_x(v_y),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_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p5410]) ).
cnf(p5427,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_c,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p5425]) ).
cnf(p5428,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_y,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5427,c11]) ).
cnf(f1,axiom,
( 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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f1_nnf,plain,
! [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) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [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) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p33,plain,
( c_in(c_Main_OsubsetI__1(X0,X1,X2),X3,X2)
| ~ c_lessequals(X0,X3,tc_set(X2))
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(p5435,plain,
( 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)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),X0,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5428,p33]) ).
cnf(p5437,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),X0,t_a),X1,t_a)
| ~ c_lessequals(v_y,X1,tc_set(t_a))
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),X0,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5435,c1]) ).
cnf(f13,negated_conjecture,
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f13_nnf,plain,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| c_lessequals(V_U,v_x(V_U),tc_set(t_a)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ c_in(X0,v_S,tc_set(t_a))
| c_lessequals(X0,v_x(X0),tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p34,plain,
c_lessequals(v_y,v_x(v_y),tc_set(t_a)),
inference(resolution,[status(thm)],[c13,c10]) ).
cnf(p5440,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),X0,t_a),v_x(v_y),t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),X0,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5437,p34]) ).
cnf(p5456,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),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))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5440,c3]) ).
cnf(p5459,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p5456]) ).
cnf(f5,axiom,
( 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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
fof(f5_nnf,plain,
! [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)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [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)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( 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(esa)],[f5_sk]) ).
cnf(p69,plain,
( c_in(c_union(c_insert(v_x(v_y),c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,v_x(v_y),t_a),v_x(v_y),tc_set(t_a))
| ~ c_in(X0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c5,p15]) ).
cnf(p390,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_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x(v_y),t_a),v_x(v_y),tc_set(t_a)) ),
inference(resolution,[status(thm)],[p69,c9]) ).
cnf(p5461,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_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5459,p390]) ).
cnf(p5514,plain,
( c_lessequals(v_x(v_y),X1,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),X1,t_a),X0,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),X0,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5461,p812]) ).
cnf(p5751,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),X0,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),X0,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p5514]) ).
cnf(p5509,plain,
( c_lessequals(v_x(v_y),X0,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x(v_y),X0,t_a),X1,t_a)
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5461,p661]) ).
cnf(p5574,plain,
( 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_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p5509]) ).
cnf(p5588,plain,
( c_lessequals(v_x(v_y),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))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5574,c3]) ).
cnf(p5595,plain,
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p5588]) ).
cnf(p5599,plain,
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5595,c11]) ).
cnf(p5773,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)
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5751,p5599]) ).
cnf(p5774,plain,
( c_in(c_Main_OsubsetI__1(v_x(v_y),v_y,t_a),v_y,t_a)
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p5773]) ).
cnf(p5781,plain,
( c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p5774,c3]) ).
cnf(p5784,plain,
c_lessequals(v_x(v_y),v_y,tc_set(t_a)),
inference(factoring,[status(thm)],[p5781]) ).
cnf(f0,axiom,
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f0_nnf,plain,
! [V_B,V_A,T_a] :
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_B,V_A,T_a] :
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p42,plain,
( v_x(v_y) = v_y
| ~ c_lessequals(v_x(v_y),v_y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p34,c0]) ).
cnf(p5786,plain,
v_x(v_y) = v_y,
inference(resolution,[status(thm)],[p5784,p42]) ).
cnf(f14,negated_conjecture,
( ~ c_in(V_U,v_S,tc_set(t_a))
| V_U != v_x(V_U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f14_nnf,plain,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| V_U != v_x(V_U) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| V_U != v_x(V_U) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ c_in(X0,v_S,tc_set(t_a))
| X0 != v_x(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p9133,plain,
( ~ c_in(v_y,v_S,tc_set(t_a))
| v_y != v_y ),
inference(superposition,[status(thm)],[p5786,c14]) ).
cnf(p9134,plain,
~ c_in(v_y,v_S,tc_set(t_a)),
inference(equality_resolution,[status(thm)],[p9133]) ).
cnf(p9135,plain,
$false,
inference(resolution,[status(thm)],[p9134,c10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET862-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n020.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 12:18:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 35.27/4.98 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.27/4.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------