%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : PUZ063-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:54:25 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 27 ( 19 unt; 0 nHn; 25 RR)
% Number of literals : 43 ( 26 equ; 18 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 17 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Set_OUn__empty__left_0,axiom,
c_union(c_emptyset,V_y,T_a) = V_y,
file('theBenchmark.p',cls_Set_OUn__empty__left_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,
( c_Mutil_Otiling(Eq_x_0,Eq_x_1) = c_Mutil_Otiling(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( tc_set(Eq_x_0) = tc_set(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_2]) ).
cnf(t2,plain,
( c_Mutil_Otiling(v_A,t_a) != c_Mutil_Otiling(v_A,t_a)
| tc_set(t_a) != tc_set(t_a)
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| v_u != c_union(c_emptyset,v_u,t_a)
| c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( c_union(c_emptyset,v_u,t_a) != v_u
| v_u = c_union(c_emptyset,v_u,t_a) ),
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_union(c_emptyset,v_u,t_a) = v_u,
inference(extension,[status(thm),parent(t4:2)],[cls_Set_OUn__empty__left_0]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
inference(extension,[status(thm),parent(t2:3)],[cls_conjecture_0]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( t_a != t_a
| tc_set(t_a) = tc_set(t_a) ),
inference(extension,[status(thm),parent(t2:4)],[equality_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:4]) ).
cnf(t12,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t10:2)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( t_a != t_a
| v_A != v_A
| c_Mutil_Otiling(v_A,t_a) = c_Mutil_Otiling(v_A,t_a) ),
inference(extension,[status(thm),parent(t2:5)],[equality_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:5]) ).
cnf(t16,plain,
v_A = v_A,
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(t18,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t14:3)],[equality_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ063-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 20:06:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------