%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET840-2 : 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 : n017.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 08:57:35 AM UTC 2026
% Result : Unsatisfiable 38.14s 38.47s
% Output : Proof 38.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 53 ( 32 unt; 4 nHn; 50 RR)
% Number of literals : 88 ( 30 equ; 35 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 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 : 35 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ c_in(V_U,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),V_U,tc_set(t_b)) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Set_OUnionI_0,axiom,
( c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_X,V_C,tc_set(T_a))
| ~ c_in(V_A,V_X,T_a) ),
file('theBenchmark.p',cls_Set_OUnionI_0) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(cls_Set_OsubsetI_0,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('theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_OsubsetI_1,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('theBenchmark.p',cls_Set_OsubsetI_1) ).
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(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_4,axiom,
( tc_set(Eq_x_0) = tc_set(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_insert(Eq_x_0,Eq_x_1,Eq_x_2) = c_insert(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_in(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_in(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,
( ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),tc_set(t_b)) ),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_1]) ).
cnf(t2,plain,
( ~ c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b))
| c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)) = c_Union(v_S,t_b)
| ~ c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),tc_set(t_b)) ),
inference(extension,[status(thm),parent(t1:1)],[cls_Set_Osubset__antisym_0]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)) != c_Union(v_S,t_b) ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)) != c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b))
| tc_set(t_b) != tc_set(t_b)
| ~ c_in(c_Union(v_S,t_b),c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_in(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_Union(v_S,t_b) != c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( c_lessequals(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b)))
| ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)) ),
inference(extension,[status(thm),parent(t6:2)],[cls_Set_OsubsetI_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
~ c_lessequals(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(extension,[status(thm),parent(t8:2)],[cls_conjecture_0]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
c_in(c_Union(v_S,t_b),c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(extension,[status(thm),parent(t6:3)],[cls_Set_OinsertCI_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t6:3]) ).
cnf(t14,plain,
( t_b != t_b
| tc_set(t_b) = tc_set(t_b) ),
inference(extension,[status(thm),parent(t6:4)],[equality_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:4]) ).
cnf(t16,plain,
t_b = t_b,
inference(extension,[status(thm),parent(t14:2)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(l7,lemma,
tc_set(t_b) = tc_set(t_b),
inference(lemma,[status(cth),parent(t6:4),below(t4:2)],[t6:4]) ).
cnf(t18,plain,
( c_emptyset != c_emptyset
| tc_set(t_b) != tc_set(t_b)
| c_Union(v_S,t_b) != c_Union(v_S,t_b)
| c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)) = c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)) ),
inference(extension,[status(thm),parent(t6:5)],[equality_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t6:5]) ).
cnf(t20,plain,
c_Union(v_S,t_b) = c_Union(v_S,t_b),
inference(extension,[status(thm),parent(t18:2)],[equality_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
tc_set(t_b) = tc_set(t_b),
inference(lemma_extension,[status(thm),parent(t18:3)],[l7:1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
c_emptyset = c_emptyset,
inference(extension,[status(thm),parent(t18:4)],[equality_1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t18:4]) ).
cnf(t26,plain,
( ~ c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),t_b),c_Union(v_S,t_b),t_b)
| c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b)) ),
inference(extension,[status(thm),parent(t2:3)],[cls_Set_OsubsetI_1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t2:3]) ).
cnf(t28,plain,
( ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),v_S,tc_set(t_b))
| ~ c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),t_b),c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),t_b)
| c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),t_b),c_Union(v_S,t_b),t_b) ),
inference(extension,[status(thm),parent(t26:2)],[cls_Set_OUnionI_0]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( c_lessequals(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),tc_set(t_b))
| c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b),t_b),c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),t_b) ),
inference(extension,[status(thm),parent(t28:2)],[cls_Set_OsubsetI_0]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
$false,
inference(reduction,[status(thm),parent(t30:2)],[t30:2,t2:3]) ).
cnf(t33,plain,
( c_lessequals(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b)))
| c_in(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),v_S,tc_set(t_b)) ),
inference(extension,[status(thm),parent(t28:3)],[cls_Set_OsubsetI_0]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t28:3]) ).
cnf(t35,plain,
~ c_lessequals(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(extension,[status(thm),parent(t33:2)],[cls_conjecture_0]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t33:2]) ).
cnf(t37,plain,
( c_lessequals(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b)))
| c_in(c_Main_OsubsetI__1(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),v_S,tc_set(t_b)) ),
inference(extension,[status(thm),parent(t1:2)],[cls_Set_OsubsetI_0]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t1:2]) ).
cnf(t39,plain,
~ c_lessequals(v_S,c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(extension,[status(thm),parent(t37:2)],[cls_conjecture_0]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t37:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET840-2 : 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
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 22:57:56 UTC 2026
% 0.08/0.37 % CPUTime :
% 38.14/38.47 % SZS status Unsatisfiable for theBenchmark
% 38.14/38.47 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------