%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET865-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 6.62s 1.27s
% Output : Proof 6.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 26 unt; 0 def)
% Number of atoms : 86 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 82 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,plain,
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(c_in(X0,X1,X2),true,ifeq(c_lessequals(X1,X3,tc_set(X2)),true,c_in(X0,X3,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f5,axiom,
c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OHausdorff_0) ).
fof(f5_nnf,plain,
! [V_S,T_a] : c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_S,T_a] : c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
c_in(c_Zorn_OHausdorff__1(X0,X1),c_Zorn_Omaxchain(X0,X1),tc_set(tc_set(X1))),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
c_in(c_Zorn_OHausdorff__1(X0,X1),c_Zorn_Omaxchain(X0,X1),tc_set(tc_set(X1))) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f7,axiom,
c_lessequals(c_Zorn_Omaxchain(V_S,T_a),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__subset__chain_0) ).
fof(f7_nnf,plain,
! [V_S,T_a] : c_lessequals(c_Zorn_Omaxchain(V_S,T_a),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_S,T_a] : c_lessequals(c_Zorn_Omaxchain(V_S,T_a),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
c_lessequals(c_Zorn_Omaxchain(X0,X1),c_Zorn_Ochain(X0,X1),tc_set(tc_set(tc_set(X1)))),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi6,axiom,
c_lessequals(c_Zorn_Omaxchain(X0,X1),c_Zorn_Ochain(X0,X1),tc_set(tc_set(tc_set(X1)))) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h0,plain,
c_in(c_Zorn_OHausdorff__1(V0,V1),c_Zorn_Ochain(V0,V1),tc_set(tc_set(V1))) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi4,hi6]) ).
cnf(f0,negated_conjecture,
( ~ c_in(V_U,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(V_U,t_a),v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
! [V_U] :
( ~ c_in(V_U,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(V_U,t_a),v_S,tc_set(t_a)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_U] :
( ~ c_in(V_U,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(V_U,t_a),v_S,tc_set(t_a)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ c_in(X0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(X0,t_a),v_S,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
ifeq(c_in(X0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),true,c_in(c_Union(X0,t_a),v_S,tc_set(t_a)),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h1,plain,
c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0]) ).
cnf(f2,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_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)],[f2]) ).
fof(f2_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)],[f2_nnf]) ).
cnf(c2,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)],[f2_sk]) ).
cnf(hi2,negated_conjecture,
ifeq(c_in(X0,v_S,tc_set(t_a)),true,c_lessequals(X0,v_x(X0),tc_set(t_a)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h2,plain,
c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),tc_set(t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h1]) ).
cnf(f1,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_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)],[f1]) ).
fof(f1_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)],[f1_nnf]) ).
cnf(c1,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)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
ifeq(c_in(X0,v_S,tc_set(t_a)),true,c_in(v_x(X0),v_S,tc_set(t_a)),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h3,plain,
c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),v_S,tc_set(t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi1,h1]) ).
cnf(f6,axiom,
( c_Union(V_c,T_a) = V_u
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__Zorn_0) ).
fof(f6_nnf,plain,
! [V_u,V_S,T_a,V_c] :
( c_Union(V_c,T_a) = V_u
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [V_u,V_S,T_a,V_c] :
( c_Union(V_c,T_a) = V_u
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_u,V_S,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( c_Union(X3,X2) = X0
| ~ c_lessequals(c_Union(X3,X2),X0,tc_set(X2))
| ~ c_in(X3,c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(c_in(X0,X1,tc_set(X2)),true,ifeq(c_in(X3,c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2))),true,ifeq(c_lessequals(c_Union(X3,X2),X0,tc_set(X2)),true,c_Union(X3,X2),X0),X0),X0) = X0,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h6,plain,
c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) = v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),
inference(hyper_resolution,[status(thm)],[hi5,h3,hi4,h2]) ).
cnf(f3,negated_conjecture,
( ~ c_in(V_U,v_S,tc_set(t_a))
| V_U != v_x(V_U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3_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)],[f3]) ).
fof(f3_sk,plain,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| V_U != v_x(V_U) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ c_in(X0,v_S,tc_set(t_a))
| X0 != v_x(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(X0,v_x(X0),ifeq(c_in(X0,v_S,tc_set(t_a)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi7,h6,h1]) ).
cnf(t69,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t69]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET865-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:17:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.62/1.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.62/1.27 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------