%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET843-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 : Thu Sep 24 08:57:36 AM UTC 2026
% Result : Unsatisfiable 3.55s 3.86s
% Output : Proof 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 65 ( 41 unt; 4 nHn; 57 RR)
% Number of literals : 106 ( 31 equ; 39 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 38 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OUnion__upper_0,axiom,
( c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a))
| ~ c_in(V_B,V_A,tc_set(T_a)) ),
file('theBenchmark.p',cls_Set_OUnion__upper_0) ).
cnf(cls_Set_Osubset__antisym_0,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('theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)),
file('theBenchmark.p',cls_Set_Osubset__refl_0) ).
cnf(cls_Zorn_OAbrial__axiom1_0,axiom,
c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
file('theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
cnf(cls_Zorn_OTFin_OsuccI_0,axiom,
( c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).
cnf(cls_Zorn_OTFin__UnionI_0,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('theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
cnf(cls_Zorn_Oeq__succ__upper_0,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('theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_2,negated_conjecture,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_9,axiom,
( c_lessequals(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_lessequals(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_1]) ).
cnf(t2,plain,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(extension,[status(thm),parent(t1:1)],[cls_conjecture_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,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)))
| c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m != c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(extension,[status(thm),parent(t2:2)],[cls_Zorn_Oeq__succ__upper_0]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(extension,[status(thm),parent(t4:2)],[cls_conjecture_0]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(l3,lemma,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(lemma,[status(cth),parent(t4:2),below(t2:2)],[t4:2]) ).
cnf(t8,plain,
( ~ c_lessequals(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a)))
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(extension,[status(thm),parent(t4:3)],[cls_Set_Osubset__antisym_0]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t1:1]) ).
cnf(t11,plain,
( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(extension,[status(thm),parent(t8:3)],[cls_Set_OUnion__upper_0]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t8:3]) ).
cnf(t13,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(lemma_extension,[status(thm),parent(t11:2)],[l3:1]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t11:2]) ).
cnf(t15,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))))
| 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))) ),
inference(extension,[status(thm),parent(t4:4)],[cls_Zorn_OTFin__UnionI_0]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t4:4]) ).
cnf(t17,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)))),
inference(extension,[status(thm),parent(t15:2)],[cls_Set_Osubset__refl_0]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(t19,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(extension,[status(thm),parent(t1:2)],[equality_3]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t1:2]) ).
cnf(t21,plain,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(extension,[status(thm),parent(t19:2)],[cls_conjecture_2]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
$false,
inference(reduction,[status(thm),parent(t21:2)],[t21:2,t1:2]) ).
cnf(t24,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a)))
| c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(extension,[status(thm),parent(t19:3)],[cls_Set_Osubset__antisym_0]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t19:3]) ).
cnf(t26,plain,
( ~ c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(extension,[status(thm),parent(t24:2)],[cls_Set_OUnion__upper_0]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(extension,[status(thm),parent(t26:2)],[cls_Zorn_OTFin_OsuccI_0]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(extension,[status(thm),parent(t28:2)],[cls_conjecture_0]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) != c_Zorn_Osucc(v_S,v_m,t_a)
| tc_set(tc_set(t_a)) != tc_set(tc_set(t_a))
| ~ c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) ),
inference(extension,[status(thm),parent(t24:3)],[equality_9]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t24:3]) ).
cnf(t34,plain,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(extension,[status(thm),parent(t32:2)],[cls_conjecture_2]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
$false,
inference(reduction,[status(thm),parent(t34:2)],[t34:2,t1:2]) ).
cnf(t37,plain,
c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(extension,[status(thm),parent(t32:3)],[cls_Zorn_OAbrial__axiom1_0]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t32:3]) ).
cnf(t39,plain,
( ~ c_lessequals(tc_set(tc_set(t_a)),tc_set(tc_set(t_a)),tc_set(U_320))
| ~ c_lessequals(tc_set(tc_set(t_a)),tc_set(tc_set(t_a)),tc_set(U_320))
| tc_set(tc_set(t_a)) = tc_set(tc_set(t_a)) ),
inference(extension,[status(thm),parent(t32:4)],[cls_Set_Osubset__antisym_0]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t32:4]) ).
cnf(t41,plain,
c_lessequals(tc_set(tc_set(t_a)),tc_set(tc_set(t_a)),tc_set(U_320)),
inference(extension,[status(thm),parent(t39:2)],[cls_Set_Osubset__refl_0]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t39:2]) ).
cnf(l21,lemma,
c_lessequals(tc_set(tc_set(t_a)),tc_set(tc_set(t_a)),tc_set(U_320)),
inference(lemma,[status(cth),parent(t39:2),below(t32:4)],[t39:2]) ).
cnf(t43,plain,
c_lessequals(tc_set(tc_set(t_a)),tc_set(tc_set(t_a)),tc_set(U_320)),
inference(lemma_extension,[status(thm),parent(t39:3)],[l21:1]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t39:3]) ).
cnf(t45,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(U_325))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(U_325))
| c_Zorn_Osucc(v_S,v_m,t_a) = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(extension,[status(thm),parent(t32:5)],[cls_Set_Osubset__antisym_0]) ).
cnf(t46,plain,
$false,
inference(connection,[status(thm),parent(t45:1)],[t45:1,t32:5]) ).
cnf(t47,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(U_325)),
inference(extension,[status(thm),parent(t45:2)],[cls_Set_Osubset__refl_0]) ).
cnf(t48,plain,
$false,
inference(connection,[status(thm),parent(t47:1)],[t47:1,t45:2]) ).
cnf(l23,lemma,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(U_325)),
inference(lemma,[status(cth),parent(t45:2),below(t32:5)],[t45:2]) ).
cnf(t49,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(U_325)),
inference(lemma_extension,[status(thm),parent(t45:3)],[l23:1]) ).
cnf(t50,plain,
$false,
inference(connection,[status(thm),parent(t49:1)],[t49:1,t45:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET843-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 23:03:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 3.55/3.86 % SZS status Unsatisfiable for theBenchmark
% 3.55/3.86 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------