%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 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 08:55:52 AM UTC 2026
% Result : Unsatisfiable 204.00s 204.38s
% Output : Proof 204.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(membership_in_subsets,axiom,
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
file('SET001-0.ax',membership_in_subsets) ).
cnf(subsets_axiom1,axiom,
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
file('SET001-0.ax',subsets_axiom1) ).
cnf(subsets_axiom2,axiom,
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
file('SET001-0.ax',subsets_axiom2) ).
cnf(set_equal_sets_are_subsets1,axiom,
( subset(Subset,Superset)
| ~ equal_sets(Subset,Superset) ),
file('SET001-0.ax',set_equal_sets_are_subsets1) ).
cnf(set_equal_sets_are_subsets2,axiom,
( subset(Subset,Superset)
| ~ equal_sets(Superset,Subset) ),
file('SET001-0.ax',set_equal_sets_are_subsets2) ).
cnf(subsets_are_set_equal_sets,axiom,
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
file('SET001-0.ax',subsets_are_set_equal_sets) ).
cnf(member_of_union_is_member_of_one_set,axiom,
( member(Element,Set2)
| member(Element,Set1)
| ~ member(Element,Union)
| ~ union(Set1,Set2,Union) ),
file('SET001-1.ax',member_of_union_is_member_of_one_set) ).
cnf(member_of_set1_is_member_of_union,axiom,
( member(Element,Union)
| ~ member(Element,Set1)
| ~ union(Set1,Set2,Union) ),
file('SET001-1.ax',member_of_set1_is_member_of_union) ).
cnf(member_of_set2_is_member_of_union,axiom,
( member(Element,Union)
| ~ member(Element,Set2)
| ~ union(Set1,Set2,Union) ),
file('SET001-1.ax',member_of_set2_is_member_of_union) ).
cnf(union_axiom1,axiom,
( member(g(Set1,Set2,Union),Union)
| member(g(Set1,Set2,Union),Set2)
| member(g(Set1,Set2,Union),Set1)
| union(Set1,Set2,Union) ),
file('SET001-1.ax',union_axiom1) ).
cnf(union_axiom2,axiom,
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set1) ),
file('SET001-1.ax',union_axiom2) ).
cnf(union_axiom3,axiom,
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set2) ),
file('SET001-1.ax',union_axiom3) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( member(Element,Set1)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('SET001-2.ax',member_of_intersection_is_member_of_set1) ).
cnf(member_of_intersection_is_member_of_set2,axiom,
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('SET001-2.ax',member_of_intersection_is_member_of_set2) ).
cnf(member_of_both_is_member_of_intersection,axiom,
( member(Element,Intersection)
| ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ),
file('SET001-2.ax',member_of_both_is_member_of_intersection) ).
cnf(intersection_axiom1,axiom,
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('SET001-2.ax',intersection_axiom1) ).
cnf(intersection_axiom2,axiom,
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('SET001-2.ax',intersection_axiom2) ).
cnf(intersection_axiom3,axiom,
( intersection(Set1,Set2,Intersection)
| ~ member(h(Set1,Set2,Intersection),Set1)
| ~ member(h(Set1,Set2,Intersection),Set2)
| ~ member(h(Set1,Set2,Intersection),Intersection) ),
file('SET001-2.ax',intersection_axiom3) ).
cnf(member_of_difference,axiom,
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
file('SET001-3.ax',member_of_difference) ).
cnf(not_member_of_difference,axiom,
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
file('SET001-3.ax',not_member_of_difference) ).
cnf(member_of_difference_or_set2,axiom,
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
file('SET001-3.ax',member_of_difference_or_set2) ).
cnf(difference_axiom2,axiom,
( member(k(Set1,Set2,Difference),Difference)
| member(k(Set1,Set2,Difference),Set1)
| difference(Set1,Set2,Difference) ),
file('SET001-3.ax',difference_axiom2) ).
cnf(difference_axiom1,axiom,
( difference(Set1,Set2,Difference)
| member(k(Set1,Set2,Difference),Difference)
| ~ member(k(Set1,Set2,Difference),Set2) ),
file('SET001-3.ax',difference_axiom1) ).
cnf(difference_axiom3,axiom,
( difference(Set1,Set2,Difference)
| member(k(Set1,Set2,Difference),Set2)
| ~ member(k(Set1,Set2,Difference),Set1)
| ~ member(k(Set1,Set2,Difference),Difference) ),
file('SET001-3.ax',difference_axiom3) ).
cnf(a_intersection_b,hypothesis,
intersection(a,b,aIb),
file('theBenchmark.p',a_intersection_b) ).
cnf(c_minus_a,hypothesis,
difference(c,a,cDa),
file('theBenchmark.p',c_minus_a) ).
cnf(c_minus_b,hypothesis,
difference(c,b,cDb),
file('theBenchmark.p',c_minus_b) ).
cnf(c_minus_aIb,hypothesis,
difference(c,aIb,cD_aIb),
file('theBenchmark.p',c_minus_aIb) ).
cnf(prove_cDa_union_cDb_is_cD_aIb,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
file('theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_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
% 0.07/0.35 % Computer : n005.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 21:26:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 204.00/204.38 % SZS status Unsatisfiable for theBenchmark
% 204.00/204.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------