%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET822-2 : 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 : n010.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 08:57:31 AM UTC 2026
% Result : Unsatisfiable 0.13s 5.74s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OemptyE_0,axiom,
~ c_in(V_a,c_emptyset,T_a),
file('theBenchmark.p',cls_Set_OemptyE_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_OinsertE_0,axiom,
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
file('theBenchmark.p',cls_Set_OinsertE_0) ).
cnf(cls_conjecture_0,negated_conjecture,
v_P(v_f(v_b)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_in(v_x(V_U,V_V),V_V,tc_IntDef_Oint)
| ~ c_in(v_f(V_U),V_V,tc_IntDef_Oint) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ v_P(v_x(V_U,V_V))
| ~ c_in(v_f(V_U),V_V,tc_IntDef_Oint) ),
file('theBenchmark.p',cls_conjecture_2) ).
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_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_4,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_5,axiom,
( v_f(Eq_x_0) = v_f(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( v_x(Eq_x_0,Eq_x_1) = v_x(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| 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(equality_8,axiom,
( v_P(Eq_y_0)
| ~ v_P(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET822-2 : 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
% 0.09/5.57 % Computer : n010.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Sat Sep 19 23:01:48 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.13/5.74 % SZS status Unsatisfiable for theBenchmark
% 0.13/5.74 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------