%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET863-2 : 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 02:44:11 PM UTC 2026
% Result : Unsatisfiable 5.06s 1.19s
% Output : Proof 5.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 81 ( 21 unt; 0 def)
% Number of atoms : 207 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 211 ( 85 ~; 126 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 147 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,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(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c6,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)],[f6_sk]) ).
cnf(f11,negated_conjecture,
c_in(v_xa,v_x,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f11_nnf,plain,
c_in(v_xa,v_x,t_a),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
c_in(v_xa,v_x,t_a),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(p58,plain,
( c_in(v_xa,X2,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X0,X2,t_a),X2,tc_set(t_a))
| ~ c_in(c_union(c_insert(v_x,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(X0,c_Zorn_Omaxchain(X1,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c6,c11]) ).
cnf(f7,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(f7_nnf,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p79,plain,
( c_in(v_xa,X0,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,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)],[p58,c7]) ).
cnf(f3,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(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,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)],[f3_sk]) ).
cnf(f9,negated_conjecture,
c_in(v_x,v_S,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f9_nnf,plain,
c_in(v_x,v_S,tc_set(t_a)),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
c_in(v_x,v_S,tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(p26,plain,
( c_in(c_union(c_insert(v_x,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,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)],[c3,c9]) ).
cnf(f8,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(f8_nnf,plain,
c_in(v_c,c_Zorn_Ochain(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_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(p30,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)],[p26,c8]) ).
cnf(p81,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,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)],[p79,p30]) ).
cnf(f5,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(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c5,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)],[f5_sk]) ).
cnf(p46,plain,
( c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X2,t_a),X0,tc_set(t_a))
| c_in(v_xa,X2,t_a)
| ~ c_in(c_union(c_insert(v_x,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(X0,c_Zorn_Omaxchain(X1,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c5,c11]) ).
cnf(p65,plain,
( 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)
| ~ 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(resolution,[status(thm)],[p46,c7]) ).
cnf(p67,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| 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)],[p65,p30]) ).
cnf(f13,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_7) ).
fof(f13_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)],[f13]) ).
fof(f13_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)],[f13_nnf]) ).
cnf(c13,plain,
( ~ c_in(X0,v_c,tc_set(t_a))
| c_lessequals(X0,v_y,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p69,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,t_a),v_c,tc_set(t_a))
| c_in(v_xa,X0,t_a) ),
inference(resolution,[status(thm)],[p67,c13]) ).
cnf(p83,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,v_y,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p81,p69]) ).
cnf(p85,plain,
( c_in(v_xa,v_y,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(factoring,[status(thm)],[p83]) ).
cnf(p86,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(factoring,[status(thm)],[p85]) ).
cnf(p88,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p86,c13]) ).
cnf(f1,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(f1_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)],[f1]) ).
fof(f1_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)],[f1_nnf]) ).
cnf(c1,plain,
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f0,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(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c0,plain,
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p18,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)],[c1,c0]) ).
cnf(p96,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X0,t_a),v_y,t_a)
| c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X0,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p88,p18]) ).
cnf(p97,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,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,t_a),X0,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p96,c0]) ).
cnf(f10,negated_conjecture,
c_lessequals(v_y,v_x,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f10_nnf,plain,
c_lessequals(v_y,v_x,tc_set(t_a)),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
c_lessequals(v_y,v_x,tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(p100,plain,
( 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))
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p97,c10]) ).
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_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
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_B,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_B,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),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p115,plain,
( 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))
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p100,c2]) ).
cnf(p118,plain,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(factoring,[status(thm)],[p115]) ).
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_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(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_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)],[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_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)],[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_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)],[f4_sk]) ).
cnf(p36,plain,
( c_in(c_union(c_insert(v_x,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,t_a),v_x,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,c9]) ).
cnf(p53,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_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p36,c8]) ).
cnf(p119,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(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p118,p53]) ).
cnf(p128,plain,
( c_in(v_xa,X0,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X0,t_a),X0,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p119,p79]) ).
cnf(p145,plain,
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(factoring,[status(thm)],[p128]) ).
cnf(p127,plain,
( 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)
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p119,p65]) ).
cnf(p131,plain,
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(factoring,[status(thm)],[p127]) ).
cnf(p139,plain,
( c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a))
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p131,c13]) ).
cnf(p155,plain,
( c_in(v_xa,v_y,t_a)
| c_in(v_xa,v_y,t_a) ),
inference(resolution,[status(thm)],[p145,p139]) ).
cnf(p156,plain,
c_in(v_xa,v_y,t_a),
inference(factoring,[status(thm)],[p155]) ).
cnf(f12,negated_conjecture,
~ c_in(v_xa,v_y,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f12_nnf,plain,
~ c_in(v_xa,v_y,t_a),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ c_in(v_xa,v_y,t_a),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ c_in(v_xa,v_y,t_a),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p157,plain,
$false,
inference(resolution,[status(thm)],[p156,c12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET863-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:18:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.06/1.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.06/1.19 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------