%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET002-1 : 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 : n001.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 08:55:50 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 29 ( 17 unt; 5 nHn; 28 RR)
% Number of literals : 49 ( 0 equ; 17 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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_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(a_union_a_is_aUa,hypothesis,
union(a,a,aUa),
file('theBenchmark.p',a_union_a_is_aUa) ).
cnf(prove_a_equals_aUa,negated_conjecture,
~ equal_sets(aUa,a),
file('theBenchmark.p',prove_a_equals_aUa) ).
cnf(t1,plain,
~ equal_sets(aUa,a),
inference(start,[status(thm),parent(0:0)],[prove_a_equals_aUa]) ).
cnf(t2,plain,
( ~ subset(aUa,a)
| ~ subset(a,aUa)
| equal_sets(aUa,a) ),
inference(extension,[status(thm),parent(t1:1)],[subsets_are_set_equal_sets]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(member_of_1_not_of_2(a,aUa),aUa)
| subset(a,aUa) ),
inference(extension,[status(thm),parent(t2:2)],[subsets_axiom2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ member(member_of_1_not_of_2(a,aUa),a)
| ~ union(a,a,aUa)
| member(member_of_1_not_of_2(a,aUa),aUa) ),
inference(extension,[status(thm),parent(t4:2)],[member_of_set2_is_member_of_union]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
union(a,a,aUa),
inference(extension,[status(thm),parent(t6:2)],[a_union_a_is_aUa]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( subset(a,aUa)
| member(member_of_1_not_of_2(a,aUa),a) ),
inference(extension,[status(thm),parent(t6:3)],[subsets_axiom1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t10:2)],[t10:2,t2:2]) ).
cnf(t13,plain,
( ~ member(member_of_1_not_of_2(aUa,a),a)
| subset(aUa,a) ),
inference(extension,[status(thm),parent(t2:3)],[subsets_axiom2]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t2:3]) ).
cnf(t15,plain,
( ~ member(member_of_1_not_of_2(aUa,a),aUa)
| member(member_of_1_not_of_2(aUa,a),a)
| ~ union(a,a,aUa)
| member(member_of_1_not_of_2(aUa,a),a) ),
inference(extension,[status(thm),parent(t13:2)],[member_of_union_is_member_of_one_set]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
union(a,a,aUa),
inference(extension,[status(thm),parent(t15:2)],[a_union_a_is_aUa]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(t19,plain,
$false,
inference(reduction,[status(thm),parent(t15:3)],[t15:3,t13:2]) ).
cnf(t20,plain,
( subset(aUa,a)
| member(member_of_1_not_of_2(aUa,a),aUa) ),
inference(extension,[status(thm),parent(t15:4)],[subsets_axiom1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t15:4]) ).
cnf(t22,plain,
$false,
inference(reduction,[status(thm),parent(t20:2)],[t20:2,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002-1 : 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
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 21:31:26 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------