TSTP Solution File: LAT005-5 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT005-5 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 11:26:38 EDT 2023
% Result : Unsatisfiable 4.75s 2.21s
% Output : Refutation 4.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 47
% Syntax : Number of formulae : 79 ( 39 unt; 16 typ; 0 def)
% Number of atoms : 119 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 464 ( 58 ~; 56 |; 0 &; 350 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 13 con; 0-3 aty)
% Number of variables : 132 ( 0 ^; 132 !; 0 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
thf(meet_type,type,
meet: $i > $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(join_type,type,
join: $i > $i > $i > $o ).
thf(r2_type,type,
r2: $i ).
thf(n1_type,type,
n1: $i ).
thf(n0_type,type,
n0: $i ).
thf(e_type,type,
e: $i ).
thf(c2_type,type,
c2: $i ).
thf(r1_type,type,
r1: $i ).
thf(d_type,type,
d: $i ).
thf(a2_type,type,
a2: $i ).
thf(b2_type,type,
b2: $i ).
thf(join_of_type,type,
join_of: $i > $i > $i ).
thf(meet_of_type,type,
meet_of: $i > $i > $i ).
thf(20,axiom,
! [A: $i] : ( meet @ n1 @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_1_and_x) ).
thf(56,plain,
! [A: $i] : ( meet @ n1 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( meet @ B @ D @ E )
| ~ ( meet @ A @ E @ F )
| ( meet @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet1) ).
thf(52,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( meet @ B @ D @ E )
| ~ ( meet @ A @ E @ F )
| ( meet @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( meet @ B @ D @ E )
| ~ ( meet @ C @ D @ F )
| ( meet @ A @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet2) ).
thf(61,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( meet @ B @ D @ E )
| ~ ( meet @ C @ D @ F )
| ( meet @ A @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( meet @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_total_function_2) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ~ ( meet @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(8,negated_conjecture,
meet @ r2 @ a @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_r2_and_a) ).
thf(41,plain,
meet @ r2 @ a @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( join @ A @ B @ C )
| ~ ( join @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_total_function_2) ).
thf(73,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( join @ A @ B @ C )
| ~ ( join @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(6,negated_conjecture,
join @ c2 @ r1 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_c2_and_r1) ).
thf(35,plain,
join @ c2 @ r1 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: $i] : ( join @ n0 @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_0_and_x) ).
thf(50,plain,
! [A: $i] : ( join @ n0 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [A: $i] : ( join @ A @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_x_and_x) ).
thf(72,plain,
! [A: $i] : ( join @ A @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(26,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ A )
| ~ ( join @ A @ C @ D )
| ~ ( meet @ C @ B @ E )
| ~ ( join @ A @ E @ F )
| ( meet @ B @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modularity2) ).
thf(68,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ A )
| ~ ( join @ A @ C @ D )
| ~ ( meet @ C @ B @ E )
| ~ ( join @ A @ E @ F )
| ( meet @ B @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(4,negated_conjecture,
meet @ r2 @ b @ e,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_r2_and_b) ).
thf(42,plain,
meet @ r2 @ b @ e,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
join @ c @ r2 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_c_and_r2) ).
thf(37,plain,
join @ c @ r2 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( join @ A @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion1) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( join @ A @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( join @ A @ B @ C )
| ~ ( join @ B @ D @ E )
| ~ ( join @ C @ D @ F )
| ( join @ A @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join2) ).
thf(57,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( join @ A @ B @ C )
| ~ ( join @ B @ D @ E )
| ~ ( join @ C @ D @ F )
| ( join @ A @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(7,negated_conjecture,
meet @ c2 @ r1 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_c2_and_r1) ).
thf(38,plain,
meet @ c2 @ r1 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,axiom,
! [A: $i] : ( meet @ n0 @ A @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_0_and_x) ).
thf(70,plain,
! [A: $i] : ( meet @ n0 @ A @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(10,negated_conjecture,
join @ r1 @ d @ b2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_r1_and_d) ).
thf(33,plain,
join @ r1 @ d @ b2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,negated_conjecture,
join @ a @ b @ c2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_a_and_b) ).
thf(32,plain,
join @ a @ b @ c2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
meet @ a @ b @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_a_and_b) ).
thf(34,plain,
meet @ a @ b @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ A )
| ~ ( join @ A @ C @ D )
| ~ ( meet @ C @ B @ E )
| ~ ( meet @ B @ D @ F )
| ( join @ A @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modularity1) ).
thf(44,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ A )
| ~ ( join @ A @ C @ D )
| ~ ( meet @ C @ B @ E )
| ~ ( meet @ B @ D @ F )
| ( join @ A @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( join @ A @ B @ C )
| ( join @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( join @ A @ B @ C )
| ( join @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,axiom,
! [A: $i] : ( join @ n1 @ A @ n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_1_and_x) ).
thf(71,plain,
! [A: $i] : ( join @ n1 @ A @ n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(18,axiom,
! [B: $i,A: $i] : ( meet @ A @ B @ ( meet_of @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_total_function_1) ).
thf(54,plain,
! [B: $i,A: $i] : ( meet @ A @ B @ ( meet_of @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( meet @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( meet @ A @ B @ C )
| ( meet @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(3,negated_conjecture,
meet @ c @ r2 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_c_and_r2) ).
thf(39,plain,
meet @ c @ r2 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( join @ A @ B @ C )
| ( meet @ A @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion2) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( join @ A @ B @ C )
| ( meet @ A @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( join @ A @ B @ C )
| ~ ( join @ B @ D @ E )
| ~ ( join @ A @ E @ F )
| ( join @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join1) ).
thf(63,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( join @ A @ B @ C )
| ~ ( join @ B @ D @ E )
| ~ ( join @ A @ E @ F )
| ( join @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(11,negated_conjecture,
~ ( meet @ a2 @ b2 @ r1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_a2_and_b2) ).
thf(40,plain,
~ ( meet @ a2 @ b2 @ r1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i] : ( meet @ A @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_x_and_x) ).
thf(55,plain,
! [A: $i] : ( meet @ A @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,negated_conjecture,
join @ r1 @ e @ a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_r1_and_e) ).
thf(36,plain,
join @ r1 @ e @ a2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [B: $i,A: $i] : ( join @ A @ B @ ( join_of @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',join_total_function_1) ).
thf(51,plain,
! [B: $i,A: $i] : ( join @ A @ B @ ( join_of @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(178,plain,
$false,
inference(e,[status(thm)],[56,52,61,65,41,73,35,50,72,68,42,37,46,57,38,70,33,32,34,44,59,71,54,76,39,48,63,40,55,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT005-5 : TPTP v8.1.2. Released v1.1.0.
% 0.11/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 18 14:40:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.87/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/0.94 % [INFO] Parsing done (147ms).
% 1.30/0.95 % [INFO] Running in sequential loop mode.
% 1.61/1.15 % [INFO] eprover registered as external prover.
% 1.61/1.15 % [INFO] cvc4 registered as external prover.
% 1.61/1.15 % [INFO] Scanning for conjecture ...
% 1.85/1.21 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 2.00/1.25 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.00/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 2.00/1.27 % [INFO] Type checking passed.
% 2.00/1.27 % [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 ...
% 4.75/2.21 % External prover 'e' found a proof!
% 4.75/2.21 % [INFO] Killing All external provers ...
% 4.75/2.21 % Time passed: 1754ms (effective reasoning time: 1257ms)
% 4.75/2.21 % 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)>
% 4.75/2.21 % Axioms used in derivation (20): join_total_function_1, meet_0_and_x, join_x_and_x, join_total_function_2, associativity_of_join2, absorbtion1, join_0_and_x, modularity2, meet_total_function_1, commutativity_of_join, absorbtion2, modularity1, meet_total_function_2, meet_1_and_x, associativity_of_meet1, commutativity_of_meet, associativity_of_join1, meet_x_and_x, join_1_and_x, associativity_of_meet2
% 4.75/2.21 % No. of inferences in proof: 63
% 4.75/2.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1754 ms resp. 1257 ms w/o parsing
% 4.84/2.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.84/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------