TSTP Solution File: SET010-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET010-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:51:51 EDT 2023
% Result : Unsatisfiable 3.30s 1.70s
% Output : Refutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 42
% Syntax : Number of formulae : 69 ( 11 unt; 16 typ; 0 def)
% Number of atoms : 145 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 628 ( 68 ~; 92 |; 0 &; 468 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 140 ( 0 ^; 140 !; 0 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_type,type,
union: $i > $i > $i > $o ).
thf(cDa_type,type,
cDa: $i ).
thf(cDb_type,type,
cDb: $i ).
thf(cD_aIb_type,type,
cD_aIb: $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(k_type,type,
k: $i > $i > $i > $i ).
thf(difference_type,type,
difference: $i > $i > $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i > $o ).
thf(member_of_1_not_of_2_type,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(h_type,type,
h: $i > $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(aIb_type,type,
aIb: $i ).
thf(g_type,type,
g: $i > $i > $i > $i ).
thf(c_type,type,
c: $i ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( difference @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_difference) ).
thf(52,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( difference @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( union @ A @ B @ C )
| ( member @ ( g @ A @ B @ C ) @ A )
| ( member @ ( g @ A @ B @ C ) @ B )
| ( member @ ( g @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom1) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( union @ A @ B @ C )
| ( member @ ( g @ A @ B @ C ) @ A )
| ( member @ ( g @ A @ B @ C ) @ B )
| ( member @ ( g @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( union @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ A )
| ( member @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).
thf(73,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( union @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ A )
| ( member @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( union @ A @ B @ C )
| ~ ( member @ D @ A )
| ( member @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).
thf(64,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( union @ A @ B @ C )
| ~ ( member @ D @ A )
| ( member @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
intersection @ a @ b @ aIb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_b) ).
thf(39,plain,
intersection @ a @ b @ aIb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
difference @ c @ b @ cDb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_b) ).
thf(66,plain,
difference @ c @ b @ cDb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ B @ C )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( subset @ B @ C )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ~ ( difference @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_member_of_difference) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( member @ A @ C )
| ~ ( difference @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ B @ C )
| ( member @ ( k @ A @ B @ C ) @ A )
| ( member @ ( k @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_axiom2) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( difference @ A @ B @ C )
| ( member @ ( k @ A @ B @ C ) @ A )
| ( member @ ( k @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
thf(58,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ C )
| ( member @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( difference @ B @ C @ D )
| ( member @ A @ D )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_difference_or_set2) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( member @ A @ B )
| ~ ( difference @ B @ C @ D )
| ( member @ A @ D )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ ( h @ A @ B @ C ) @ C )
| ( intersection @ A @ B @ C )
| ( member @ ( h @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom1) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( h @ A @ B @ C ) @ C )
| ( intersection @ A @ B @ C )
| ( member @ ( h @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ ( h @ A @ B @ C ) @ C )
| ( intersection @ A @ B @ C )
| ( member @ ( h @ A @ B @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom2) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ ( h @ A @ B @ C ) @ C )
| ( intersection @ A @ B @ C )
| ( member @ ( h @ A @ B @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( k @ A @ B @ C ) @ C )
| ~ ( member @ ( k @ A @ B @ C ) @ A )
| ( member @ ( k @ A @ B @ C ) @ B )
| ( difference @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_axiom3) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( k @ A @ B @ C ) @ C )
| ~ ( member @ ( k @ A @ B @ C ) @ A )
| ( member @ ( k @ A @ B @ C ) @ B )
| ( difference @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,axiom,
difference @ c @ aIb @ cD_aIb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_aIb) ).
thf(70,plain,
difference @ c @ aIb @ cD_aIb,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ A @ B ) @ B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( member_of_1_not_of_2 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( member_of_1_not_of_2 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,negated_conjecture,
~ ( union @ cDa @ cDb @ cD_aIb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
thf(27,plain,
~ ( union @ cDa @ cDb @ cD_aIb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( union @ A @ B @ C )
| ~ ( member @ D @ B )
| ( member @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set2_is_member_of_union) ).
thf(71,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( union @ A @ B @ C )
| ~ ( member @ D @ B )
| ( member @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( k @ A @ B @ C ) @ B )
| ( member @ ( k @ A @ B @ C ) @ C )
| ( difference @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_axiom1) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( k @ A @ B @ C ) @ B )
| ( member @ ( k @ A @ B @ C ) @ C )
| ( difference @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( h @ A @ B @ C ) @ C )
| ~ ( member @ ( h @ A @ B @ C ) @ B )
| ~ ( member @ ( h @ A @ B @ C ) @ A )
| ( intersection @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom3) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( h @ A @ B @ C ) @ C )
| ~ ( member @ ( h @ A @ B @ C ) @ B )
| ~ ( member @ ( h @ A @ B @ C ) @ A )
| ( intersection @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
difference @ c @ a @ cDa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_a) ).
thf(67,plain,
difference @ c @ a @ cDa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ B )
| ~ ( member @ D @ A )
| ( member @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( intersection @ A @ B @ C )
| ~ ( member @ D @ B )
| ~ ( member @ D @ A )
| ( member @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( g @ A @ B @ C ) @ A )
| ~ ( member @ ( g @ A @ B @ C ) @ C )
| ( union @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom2) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( g @ A @ B @ C ) @ A )
| ~ ( member @ ( g @ A @ B @ C ) @ C )
| ( union @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( g @ A @ B @ C ) @ B )
| ~ ( member @ ( g @ A @ B @ C ) @ C )
| ( union @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom3) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ ( g @ A @ B @ C ) @ B )
| ~ ( member @ ( g @ A @ B @ C ) @ C )
| ( union @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(75,plain,
$false,
inference(e,[status(thm)],[56,52,60,73,64,39,66,35,48,40,58,42,37,46,29,70,33,44,27,71,54,50,67,31,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 19:02:18 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.89/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.97 % [INFO] Parsing done (138ms).
% 1.23/0.98 % [INFO] Running in sequential loop mode.
% 1.64/1.17 % [INFO] eprover registered as external prover.
% 1.64/1.17 % [INFO] cvc4 registered as external prover.
% 1.64/1.18 % [INFO] Scanning for conjecture ...
% 1.93/1.23 % [INFO] Found a conjecture and 28 axioms. Running axiom selection ...
% 1.94/1.27 % [INFO] Axiom selection finished. Selected 25 axioms (removed 3 axioms).
% 1.94/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.94/1.30 % [INFO] Type checking passed.
% 2.22/1.30 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.30/1.70 % External prover 'e' found a proof!
% 3.30/1.70 % [INFO] Killing All external provers ...
% 3.30/1.70 % Time passed: 1190ms (effective reasoning time: 718ms)
% 3.30/1.70 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.30/1.70 % Axioms used in derivation (25): member_of_intersection_is_member_of_set2, member_of_difference_or_set2, subsets_axiom2, member_of_intersection_is_member_of_set1, union_axiom2, difference_axiom1, intersection_axiom1, not_member_of_difference, member_of_difference, member_of_union_is_member_of_one_set, union_axiom3, difference_axiom3, member_of_both_is_member_of_intersection, member_of_set2_is_member_of_union, c_minus_a, difference_axiom2, c_minus_aIb, intersection_axiom3, intersection_axiom2, union_axiom1, c_minus_b, a_intersection_b, member_of_set1_is_member_of_union, membership_in_subsets, subsets_axiom1
% 3.30/1.70 % No. of inferences in proof: 53
% 3.30/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1190 ms resp. 718 ms w/o parsing
% 3.30/1.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.30/1.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------