%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET844-2 : 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 02:44:06 PM UTC 2026
% Result : Unsatisfiable 3.66s 1.44s
% Output : Proof 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 27 unt; 0 def)
% Number of atoms : 51 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 45 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f0_nnf,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
c_lessequals(X0,X0,tc_set(X1)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h1,plain,
c_lessequals(c_Zorn_OTFin(v_S,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0]) ).
cnf(f1,axiom,
( c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
fof(f1_nnf,plain,
! [V_Y,V_S,T_a] :
( c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_Y,V_S,T_a] :
( c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))),true,c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h2,plain,
c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(hyper_resolution,[status(thm)],[hi1,h1]) ).
cnf(f3,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3_nnf,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(hi3,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h0,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) = true,
inference(hyper_resolution,[status(thm)],[hi3]) ).
cnf(f2,axiom,
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| V_m != c_Zorn_Osucc(V_S,V_m,T_a)
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).
fof(f2_nnf,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| V_m != c_Zorn_Osucc(V_S,V_m,T_a)
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| V_m != c_Zorn_Osucc(V_S,V_m,T_a)
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| X0 != c_Zorn_Osucc(X1,X0,X2)
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))),true,ifeq(c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))),true,ifeq(X0,c_Zorn_Osucc(X1,X0,X2),c_lessequals(X3,X0,tc_set(tc_set(X2))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f4,negated_conjecture,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4_nnf,plain,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t4,plain,
c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0,h2,hi4]) ).
cnf(t16,plain,
c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f5,negated_conjecture,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5_nnf,plain,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) != true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t16]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET844-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.93 % Computer : n020.cluster.edu
% 0.09/0.93 % Model : x86_64 x86_64
% 0.09/0.93 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.93 % Memory : 8046.5625MB
% 0.09/0.93 % OS : Linux 6.8.0-71-generic
% 0.09/0.93 % CPULimit : 300
% 0.09/0.93 % WCLimit : 300
% 0.09/0.93 % DateTime : Thu Sep 24 12:12:06 UTC 2026
% 0.09/0.93 % CPUTime :
% 0.09/0.93 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.66/1.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.66/1.44 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------