%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET864-2 : 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 5.21s 1.16s
% Output : Proof 5.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 60 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 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 : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,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_4) ).
fof(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,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)],[f4_sk]) ).
cnf(hi4,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)],[c4]) ).
cnf(f2,negated_conjecture,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi2,negated_conjecture,
c_in(c_Union(v_c,t_a),v_S,tc_set(t_a)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h0,plain,
c_lessequals(c_Union(v_c,t_a),v_x(c_Union(v_c,t_a)),tc_set(t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi2]) ).
cnf(f3,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_3) ).
fof(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,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)],[f3_sk]) ).
cnf(hi3,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)],[c3]) ).
cnf(h1,plain,
c_in(v_x(c_Union(v_c,t_a)),v_S,tc_set(t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi2]) ).
cnf(f0,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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__Zorn_0) ).
fof(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c0,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)],[f0_sk]) ).
cnf(hi0,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)],[c0]) ).
cnf(f1,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(f1_nnf,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi1,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h4,plain,
c_Union(v_c,t_a) = v_x(c_Union(v_c,t_a)),
inference(hyper_resolution,[status(thm)],[hi0,h1,hi1,h0]) ).
cnf(f5,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_5) ).
fof(f5_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)],[f5]) ).
fof(f5_sk,plain,
! [V_U] :
( ~ c_in(V_U,v_S,tc_set(t_a))
| V_U != v_x(V_U) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ c_in(X0,v_S,tc_set(t_a))
| X0 != v_x(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,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)],[c5]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi5,h4,hi2]) ).
cnf(t37,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t37]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET864-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:18:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.21/1.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.21/1.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------