%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET014-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n006.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 08:55:54 AM UTC 2026
% Result : Unsatisfiable 125.12s 125.50s
% Output : Proof 129.01s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(a2,axiom,
( little_set(X)
| ~ member(X,Y) ),
file('theBenchmark.p',a2) ).
cnf(extensionality1,axiom,
( X = Y
| little_set(f1(X,Y)) ),
file('theBenchmark.p',extensionality1) ).
cnf(extensionality2,axiom,
( X = Y
| member(f1(X,Y),Y)
| member(f1(X,Y),X) ),
file('theBenchmark.p',extensionality2) ).
cnf(extensionality3,axiom,
( X = Y
| ~ member(f1(X,Y),Y)
| ~ member(f1(X,Y),X) ),
file('theBenchmark.p',extensionality3) ).
cnf(intersection1,axiom,
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('theBenchmark.p',intersection1) ).
cnf(intersection2,axiom,
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('theBenchmark.p',intersection2) ).
cnf(intersection3,axiom,
( ~ member(Z,Y)
| ~ member(Z,X)
| member(Z,intersection(X,Y)) ),
file('theBenchmark.p',intersection3) ).
cnf(complement1,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('theBenchmark.p',complement1) ).
cnf(complement2,axiom,
( member(Z,X)
| ~ little_set(Z)
| member(Z,complement(X)) ),
file('theBenchmark.p',complement2) ).
cnf(union,axiom,
union(X,Y) = complement(intersection(complement(X),complement(Y))),
file('theBenchmark.p',union) ).
cnf(empty_set,axiom,
~ member(Z,empty_set),
file('theBenchmark.p',empty_set) ).
cnf(universal_set,axiom,
( ~ little_set(Z)
| member(Z,universal_set) ),
file('theBenchmark.p',universal_set) ).
cnf(subset1,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subset(X,Y) ),
file('theBenchmark.p',subset1) ).
cnf(subset2,axiom,
( member(f17(X,Y),X)
| subset(X,Y) ),
file('theBenchmark.p',subset2) ).
cnf(subset3,axiom,
( ~ member(f17(X,Y),Y)
| subset(X,Y) ),
file('theBenchmark.p',subset3) ).
cnf(a_subset_of_c,hypothesis,
subset(as,cs),
file('theBenchmark.p',a_subset_of_c) ).
cnf(b_subset_of_c,hypothesis,
subset(bs,cs),
file('theBenchmark.p',b_subset_of_c) ).
cnf(prove_a_union_b_subset_of_c,negated_conjecture,
~ subset(union(as,bs),cs),
file('theBenchmark.p',prove_a_union_b_subset_of_c) ).
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,
( f1(Eq_x_0,Eq_x_1) = f1(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,
( intersection(Eq_x_0,Eq_x_1) = intersection(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( complement(Eq_x_0) = complement(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( union(Eq_x_0,Eq_x_1) = union(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( f17(Eq_x_0,Eq_x_1) = f17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( member(Eq_y_0,Eq_y_1)
| ~ member(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( little_set(Eq_y_0)
| ~ little_set(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET014-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 21:26:12 UTC 2026
% 0.10/0.36 % CPUTime :
% 125.12/125.50 % SZS status Unsatisfiable for theBenchmark
% 125.12/125.50 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------