TSTP Solution File: LAT037-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LAT037-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 2.82s 1.61s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 27
% Syntax : Number of formulae : 48 ( 39 unt; 7 typ; 0 def)
% Number of atoms : 43 ( 42 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 170 ( 4 ~; 2 |; 0 &; 164 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(yy_type,type,
yy: $i ).
thf(zz_type,type,
zz: $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(join_type,type,
join: $i > $i > $i ).
thf(n1_type,type,
n1: $i ).
thf(n0_type,type,
n0: $i ).
thf(xx_type,type,
xx: $i ).
thf(18,axiom,
( ( meet @ xx @ zz )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs4) ).
thf(57,plain,
( ( meet @ xx @ zz )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
( ( meet @ xx @ yy )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs3) ).
thf(61,plain,
( ( meet @ xx @ yy )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ ( meet @ A @ B ) @ C )
= ( meet @ A @ ( meet @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
thf(53,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)],[16]) ).
thf(14,axiom,
! [A: $i] :
( ( join @ A @ n0 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).
thf(49,plain,
! [A: $i] :
( ( join @ A @ n0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( meet @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
thf(42,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)],[11]) ).
thf(2,axiom,
! [A: $i] :
( ( meet @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
thf(24,plain,
! [A: $i] :
( ( meet @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
yy != zz,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rhs) ).
thf(21,plain,
yy != zz,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [A: $i] :
( ( meet @ A @ n1 )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_1) ).
thf(28,plain,
! [A: $i] :
( ( meet @ A @ n1 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] :
( ( meet @ A @ n0 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_0) ).
thf(38,plain,
! [A: $i] :
( ( meet @ A @ n0 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( meet @ B @ C ) )
= ( meet @ ( join @ A @ B ) @ ( join @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_join) ).
thf(34,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)],[7]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ A @ B )
!= A )
| ( ( meet @ B @ ( join @ A @ C ) )
= ( join @ A @ ( meet @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( ( meet @ A @ B )
!= A )
| ( ( meet @ B @ ( join @ A @ C ) )
= ( join @ A @ ( meet @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
( ( join @ xx @ yy )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs1) ).
thf(59,plain,
( ( join @ xx @ yy )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( meet @ A @ ( join @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( join @ A @ ( meet @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
( ( join @ xx @ zz )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs2) ).
thf(55,plain,
( ( join @ xx @ zz )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
! [A: $i] :
( ( join @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
thf(36,plain,
! [A: $i] :
( ( join @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i] :
( ( join @ A @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_1) ).
thf(30,plain,
! [A: $i] :
( ( join @ A @ n1 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( meet @ A @ ( join @ B @ C ) )
= ( join @ ( meet @ A @ B ) @ ( meet @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_meet) ).
thf(51,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)],[15]) ).
thf(63,plain,
$false,
inference(e,[status(thm)],[57,61,53,49,47,42,24,21,28,38,32,34,44,59,40,26,55,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT037-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 14:33:58 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.94/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (121ms).
% 1.19/0.97 % [INFO] Running in sequential loop mode.
% 1.67/1.16 % [INFO] eprover registered as external prover.
% 1.67/1.16 % [INFO] cvc4 registered as external prover.
% 1.67/1.16 % [INFO] Scanning for conjecture ...
% 1.67/1.21 % [INFO] Found a conjecture and 19 axioms. Running axiom selection ...
% 1.90/1.25 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 1.90/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.90/1.27 % [INFO] Type checking passed.
% 1.90/1.27 % [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 ...
% 2.82/1.61 % External prover 'e' found a proof!
% 2.82/1.61 % [INFO] Killing All external provers ...
% 2.82/1.61 % Time passed: 1096ms (effective reasoning time: 641ms)
% 2.82/1.61 % 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)>
% 2.82/1.61 % Axioms used in derivation (19): commutativity_of_join, lhs1, commutativity_of_meet, x_meet_1, associativity_of_join, idempotence_of_meet, lhs3, dist_join, absorption1, x_join_1, modular, associativity_of_meet, lhs4, idempotence_of_join, absorption2, lhs2, x_join_0, x_meet_0, dist_meet
% 2.82/1.61 % No. of inferences in proof: 41
% 2.82/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1096 ms resp. 641 ms w/o parsing
% 2.82/1.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.82/1.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------