TSTP Solution File: LAT038-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT038-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 11:26:43 EDT 2023
% Result : Unsatisfiable 3.18s 1.76s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 25
% Syntax : Number of formulae : 43 ( 35 unt; 8 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 210 ( 2 ~; 0 |; 0 &; 208 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_type,type,
f: $i > $i > $i ).
thf(aa_type,type,
aa: $i ).
thf(dd_type,type,
dd: $i ).
thf(cc_type,type,
cc: $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(join_type,type,
join: $i > $i > $i ).
thf(bb_type,type,
bb: $i ).
thf(n0_type,type,
n0: $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
( ( f @ ( join @ aa @ bb ) @ dd )
= ( f @ ( join @ cc @ bb ) @ dd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs1) ).
thf(41,plain,
( ( f @ ( join @ aa @ bb ) @ dd )
= ( f @ ( join @ cc @ bb ) @ dd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( f @ n0 @ A )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_left_bottom) ).
thf(45,plain,
! [A: $i] :
( ( f @ n0 @ A )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(27,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( f @ ( join @ A @ B ) @ C )
= ( join @ ( f @ A @ C ) @ ( f @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_left_join) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( f @ ( join @ A @ B ) @ C )
= ( join @ ( f @ A @ C ) @ ( f @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( f @ aa @ dd )
!= ( f @ cc @ dd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rhs) ).
thf(18,plain,
( ( f @ aa @ dd )
!= ( f @ cc @ dd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( f @ A @ ( join @ B @ C ) )
= ( join @ ( f @ A @ B ) @ ( f @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_right_join) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( f @ A @ ( join @ B @ C ) )
= ( join @ ( f @ A @ B ) @ ( f @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: $i] :
( ( f @ A @ n0 )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_right_bottom) ).
thf(51,plain,
! [A: $i] :
( ( f @ A @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
( ( meet @ ( f @ aa @ dd ) @ ( f @ bb @ dd ) )
= ( meet @ ( f @ cc @ dd ) @ ( f @ bb @ dd ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs2) ).
thf(47,plain,
( ( meet @ ( f @ aa @ dd ) @ ( f @ bb @ dd ) )
= ( meet @ ( f @ cc @ dd ) @ ( f @ bb @ dd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ C ) )
= ( join @ ( meet @ A @ B ) @ ( meet @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_meet) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ C ) )
= ( join @ ( meet @ A @ B ) @ ( meet @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( meet @ B @ C ) )
= ( meet @ ( join @ A @ B ) @ ( join @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_join) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( meet @ B @ C ) )
= ( meet @ ( join @ A @ B ) @ ( join @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(21,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(65,plain,
$false,
inference(cvc4,[status(thm)],[29,41,45,27,49,39,35,18,31,43,23,51,47,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT038-1 : TPTP v8.1.2. Released v2.4.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n020.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Thu May 18 14:16:48 EDT 2023
% 0.17/0.37 % CPUTime :
% 1.00/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.99 % [INFO] Parsing done (122ms).
% 1.26/1.00 % [INFO] Running in sequential loop mode.
% 1.71/1.19 % [INFO] eprover registered as external prover.
% 1.71/1.20 % [INFO] cvc4 registered as external prover.
% 1.71/1.20 % [INFO] Scanning for conjecture ...
% 1.88/1.25 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.88/1.29 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.88/1.31 % [INFO] Problem is propositional (TPTP CNF).
% 1.88/1.31 % [INFO] Type checking passed.
% 2.10/1.31 % [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 ...
% 3.18/1.75 % External prover 'cvc4' found a proof!
% 3.18/1.75 % [INFO] Killing All external provers ...
% 3.18/1.75 % Time passed: 1217ms (effective reasoning time: 749ms)
% 3.18/1.75 % 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)>
% 3.18/1.76 % Axioms used in derivation (16): f_on_right_bottom, commutativity_of_join, absorption1, lhs1, f_on_right_join, commutativity_of_meet, lhs2, associativity_of_join, idempotence_of_meet, dist_meet, dist_join, f_on_left_join, associativity_of_meet, f_on_left_bottom, idempotence_of_join, absorption2
% 3.18/1.76 % No. of inferences in proof: 35
% 3.18/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1217 ms resp. 749 ms w/o parsing
% 3.39/1.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.39/1.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------