%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL431-2 : 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 : n005.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 08:49:16 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 20 unt; 0 nHn; 25 RR)
% Number of literals : 48 ( 26 equ; 20 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 25 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_PropLog_Osat(c_emptyset,v_p,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_PropLog_Ocompleteness__0__lemma__dest_0,axiom,
( c_in(V_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(V_p,V_U,T_a),c_PropLog_Ohyps(V_p,V_t0,T_a),tc_set(tc_PropLog_Opl(T_a))),T_a),tc_PropLog_Opl(T_a))
| ~ c_PropLog_Osat(c_emptyset,V_p,T_a) ),
file('theBenchmark.p',cls_PropLog_Ocompleteness__0__lemma__dest_0) ).
cnf(cls_Set_ODiff__cancel_0,axiom,
c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset,
file('theBenchmark.p',cls_Set_ODiff__cancel_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_PropLog_Othms(Eq_x_0,Eq_x_1) = c_PropLog_Othms(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_PropLog_Opl(Eq_x_0) = tc_PropLog_Opl(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_1]) ).
cnf(t2,plain,
( c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,U_231,t_a),c_PropLog_Ohyps(v_p,U_231,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a) != c_PropLog_Othms(c_emptyset,t_a)
| tc_PropLog_Opl(t_a) != tc_PropLog_Opl(t_a)
| ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,U_231,t_a),c_PropLog_Ohyps(v_p,U_231,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| v_p != v_p
| c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)) ),
inference(extension,[status(thm),parent(t1:1)],[equality_10]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( v_p != v_p
| v_p = v_p ),
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,
v_p = v_p,
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ c_PropLog_Osat(c_emptyset,v_p,t_a)
| c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,U_231,t_a),c_PropLog_Ohyps(v_p,U_231,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(extension,[status(thm),parent(t2:3)],[cls_PropLog_Ocompleteness__0__lemma__dest_0]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
c_PropLog_Osat(c_emptyset,v_p,t_a),
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,
( t_a != t_a
| tc_PropLog_Opl(t_a) = tc_PropLog_Opl(t_a) ),
inference(extension,[status(thm),parent(t2:4)],[equality_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t12:2)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( t_a != t_a
| c_minus(c_PropLog_Ohyps(v_p,U_231,t_a),c_PropLog_Ohyps(v_p,U_231,t_a),tc_set(tc_PropLog_Opl(t_a))) != c_emptyset
| c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,U_231,t_a),c_PropLog_Ohyps(v_p,U_231,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a) = c_PropLog_Othms(c_emptyset,t_a) ),
inference(extension,[status(thm),parent(t2:5)],[equality_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:5]) ).
cnf(t18,plain,
c_minus(c_PropLog_Ohyps(v_p,U_231,t_a),c_PropLog_Ohyps(v_p,U_231,t_a),tc_set(tc_PropLog_Opl(t_a))) = c_emptyset,
inference(extension,[status(thm),parent(t16:2)],[cls_Set_ODiff__cancel_0]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
t_a = t_a,
inference(extension,[status(thm),parent(t16:3)],[equality_1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % 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 : n005.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 15:02:03 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------